Free Printable Physics based Calculus

1.

Find the derivtives of

$f\left(x\right)\ =\ \left(x^2+x\right)\left(2x+5\right)$

a)

$2x^2+12x+5$

b)

$6x^2-14x+5$

c)

$2x^2+14x+5$

d)

$6x^2+14x+5$

2.

Find the derivative

$f\left(x\right)=\ \left(4x+2\right)\left(2x^3+x^2\right)$

a)

$32x^3-24x^2-4x$

b)

$32x^3+24x^2+4x$

c)

$22x^3+24x^2+4x$

d)

$32x^3-24x^2+4x$

3.

Find the derivative of $\frac{x^2+x}{2x+1}$

a)

$\frac{4x^2+2x+2}{2x^2+4x+1}$

b)

$\frac{2x^2-2x-1}{4x^2+4x-1}$

c)

$\frac{2x^2+2x+1}{4x^2+4x+1}$

d)

$\frac{2x^2+2x+1}{2x^2+4x-1}$

4.

Find the derivative of $\sqrt[]{4x}$

a)

$\frac{1}{\sqrt[]{x}}$

b)

$\frac{-1}{\sqrt[]{x}}$

c)

$\frac{1}{\sqrt[]{2x}}$

d)

$\frac{4}{\sqrt[]{x}}$

5.

Find the derivative of $\frac{x^2+4x+4}{x+2}$

a)

x+2

b)

$1$

c)

2

d)

x+1

6.

Find the derivatives of $\frac{\sqrt[]{x}}{4x}$

a)

$\frac{1}{8\sqrt[]{x^3}}$

b)

$\frac{-1}{8\sqrt[]{x^3}}$

c)

$\frac{-1}{\sqrt[]{x^3}}$

d)

$\frac{-1}{2\sqrt[]{x^3}}$

7.

$\left(x^2+2\right)\left(2x+4\right)$

Find the derivative of

a)

$6x^2+8x+4$

b)

$6x^2-8x-4$

c)

$6x^2-8x+4$

d)

$4x^2+8x+3$

8.

find the derivative of $\frac{\sqrt[]{2}}{x^2}$

a)

$\frac{2\ \sqrt[]{2}}{x^3}$

b)

$\frac{-\sqrt[]{2}}{x^3}$

c)

$\frac{\ \sqrt[]{2}}{x^3}$

d)

$\frac{-2\ \sqrt[]{2}}{x^3}$

9.

$\frac{x}{4}+\frac{4}{x}$

Find the derivative of

a)

$\frac{1}{4}-\frac{2}{x^2}$

b)

$\frac{1}{4}+\frac{4}{x^2}$

c)

$\frac{1}{4}-\frac{4}{x^2}$

d)

$\frac{1}{4}+\frac{2}{x^2}$

10.

$\frac{4x^3-2x-10}{3x^2+5x-2}$

Find the derivatives of

a)

$\frac{12x^4+40x^3-18x^2+60x+54}{\left(3x^2+5x-2\right)^2}$

b)

$\frac{62x^4-40x^3+18x^2-60x+54}{\left(3x^2+5x-2\right)^2}$

c)

$\frac{62x^4-40x^3+18x^2+60x+18}{\left(3x^2+5x-2\right)^2}$

d)

$\frac{x^4+x^3-x^2+10x+54}{\left(3x^2+5x-2\right)^2}$

11.

$\sqrt[]{x^2+1}$

Find the derivative

a)

$\frac{x}{\sqrt[]{x^2+1}}$

b)

$\frac{-x}{\sqrt[]{x^2+1}}$

c)

$\frac{3x}{\sqrt[]{x^2+1}}$

d)

$\frac{x}{\sqrt[]{x^2-1}}$

12.

$2x^4\left(3x^2-5\right)^6$

Find the derivative of

a)

$8x^3\left(3x^2-5\right)^6-72x^5\left(3x^2-5\right)^5$

b)

$4x^3\left(3x^2-5\right)^6+62x^5\left(3x^2-5\right)^5$

c)

$2x^3\left(3x^2-5\right)^6-62x^5\left(3x^2-5\right)^5$

d)

$8x^3\left(3x^2-5\right)^6+72x^5\left(3x^2-5\right)^5$

13.

$\left(\frac{x-2}{2x+1}\right)^9$

Find the derivative of

a)

$\frac{\left(x-2\right)^9}{\left(2x+1\right)^{10}}$

b)

$\frac{-\left(x-2\right)^9}{\left(2x+1\right)^{10}}$

c)

$\frac{45\left(x-2\right)^8}{\left(2x+1\right)^{10}}$

d)

$\frac{10\left(x-2\right)^8}{\left(2x+1\right)^{10}}$

14.

Find the derivative $\tan\left(\cos\left(\sin\left(\frac{x}{2}\right)\right)\right)$

a)

$\left(-\frac{1}{2}\right)\cdot\sec^2\left(\cos\left(\sin\left(\frac{x}{2}\right)\right)\right)\cdot\left(\sin\left(\sin\left(\frac{x}{2}\right)\right)\right)\cdot\cos\left(\frac{x}{2}\right)$

b)

$\left(-\frac{1}{2}\right)\cdot\sec^2\left(\cos\left(\sin\left(x\right)\right)\right)\cdot\left(\sin\left(\sin\left(x\right)\right)\right)\cdot\cos\left(x\right)$

c)

$\left(-\frac{1}{2}\right)\cdot\tan\left(\tan\left(\sin\left(\frac{x}{2}\right)\right)\right)\cdot\left(\sin\left(\cos\left(\frac{x}{2}\right)\right)\right)\cdot\cos\left(\frac{x}{2}\right)$

d)

$\sec^2\left(\cos\left(\sin\left(\frac{x}{2}\right)\right)\right)\cdot\left(\sin\left(\sin\left(\frac{x}{2}\right)\right)\right)\cdot\cos\left(\frac{x}{2}\right)$

15.

Find the derivative $\left[5\sin x-4\tan x\right]$

a)

$5\cos\left(x\right)+4\sec^2\left(x\right)$

b)

$4\cos\left(x\right)-5\sec^2\left(x\right)$

c)

$5\cos\left(x\right)-4\sec^2\left(x\right)$

d)

$4\cos\left(x\right)+5\sec^2\left(x\right)$

16.

Find the derivative $\left(\tan x\right)\left(\sec x\right)$

a)

$\tan^2\left(x\right)\sec\left(x\right)-\sec^3\left(x\right)$

b)

$\tan^2\left(x\right)\sec\left(x\right)+\sec^3\left(x\right)$

c)

$\tan^2\left(x\right)\sec\left(x\right)+\tan\sec^3\left(x\right)$

d)

$\sec\left(x\right)+\sec^3\left(x\right)$

17.

find the derivative $\frac{2\csc\left(x\right)-1}{\csc\left(x\right)+2}$

a)

$\frac{-5\csc\left(x\right)\cot\left(x\right)}{\left(\csc\left(x\right)+2\right)^2}$

b)

$\frac{-2\csc\left(x\right)\cot\left(x\right)}{\left(\csc\left(x\right)+2\right)^2}$

c)

$\frac{-2\csc\left(x\right)\cot\left(x\right)}{\left(\csc\left(x\right)+2\right)^2}$

d)

$\frac{5\csc\left(x\right)\cot\left(x\right)}{\left(\csc\left(x\right)+2\right)^2}$

18.

Find the derivative $\sqrt[4]{\left(2x^2+7\right)^3}$

a)

$\frac{3x}{\sqrt[4]{2x^2+7}}$

b)

$\frac{-3x}{\sqrt[4]{2x^2+7}}$

c)

$\frac{-x}{\sqrt[4]{2x^2+7}}$

d)

$\frac{5}{\sqrt[4]{2x^2+7}}$

19.

Find the derivative of $\log_4x^2$

a)

$\frac{1}{x\ln2}$

b)

$\frac{3}{x\ln4}$

c)

$\frac{2}{x\ln4}$

d)

$\frac{2}{x\ln3}$

20.

$\log_2\left(3x-x^4\right)$

Find the derivative

a)

$\frac{3+4x^3}{\left(3x-x^4\right)\ln2}$

b)

$\frac{4x^3}{\left(3x-x^4\right)\ln2}$

c)

$\frac{-4x^3}{\left(3x-x^4\right)\ln2}$

d)

$\frac{3-4x^3}{\left(3x-x^4\right)\ln2}$

21.

$5^{\left(2x-x^2\right)}$

Find the derivative of the exponential

a)

$5^{\left(2x-x^2\right)}\left(2-2x\right)\left(\ln\left(5\right)\right)$

b)

$5^{\left(2x-x^2\right)}\left(2-2x\right)\left(\ln\left(2\right)\right)$

c)

$5^{\left(2x-x^2\right)}\left(2+2x\right)\left(\ln\left(5\right)\right)$

d)

$5^{\left(2x-x^2\right)}\left(1-2x\right)\left(\ln\left(5\right)\right)$

22.

$e^{\left(3x^4-2x^2+\text{4}\right)}$

Find the derivative of the exponential

a)

$\left(12x^3-4x\right)e^{\left(3x^4-2x^2+\text{4}\right)}$

b)

$\left(-12x^3-4x\right)e^{\left(3x^4-2x^2+\text{4}\right)}$

c)

$\left(12x^3+4x\right)e^{\left(3x^4-2x^2+\text{4}\right)}$

d)

$\left(3x^3-4x\right)e^{\left(3x^4-2x^2+\text{4}\right)}$

23.

Find the derivative of $\sqrt[]{\frac{2x}{x^3-2x}}$

(Difficulty: Extreme) If answered right additional 1 deduction to list :"(

a)

$\frac{2x}{\left(\sqrt[]{\left(x^2-3\right)^3}\right)}$

b)

$\frac{-2x}{\left(\sqrt[]{2}\right)\left(\sqrt[]{\left(x^2-3\right)^3}\right)}$

c)

$\frac{-2x}{\left(\sqrt[]{\left(x^2-3\right)^3}\right)}$

d)

$\frac{x}{\left(\sqrt[]{2}\right)\left(\sqrt[]{\left(x^2-3\right)^3}\right)}$

Physics based Calculus

Total questions: 23

Worksheet time: 6hrs 45mins

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