Free Printable (M2W6.2) QUIZ - Differentiating; Product [QUIZIZZ]

1.

Let $y=x^4\ln\left(x\right)$

Find $\frac{dy}{dx}$

a)

$x^3\left(4\ln\left(x\right)+1\right)$

b)

$4x^3\left(x^4+\ln\left(x\right)\right)$

c)

$4x^3+\frac{1}{x}$

d)

$4x^2$

2.

Find $\frac{d}{dx}\left(\ln\left(x\right)e^x\right)$

a)

$e^x\left(\frac{1}{x}+\ln\left(x\right)\right)$

b)

$\frac{1}{x}+e^x$

c)

$\frac{e^x}{x}+\ln\left(x\right)$

d)

$\frac{e^x}{x}$

3.

THE ANSWER IS A WHOLE NUMBER, DO NOT WRITE DOWN ANY DECIMALS

Let $g$ be a function such that $g\left(4\right)=8$ and $g'\left(4\right)=-3$

Let $h\left(x\right)=\sqrt[]{x}$

And let $H\left(x\right)=g\left(x\right)\cdot h\left(x\right)$

Calculate $H'\left(4\right)$

(a)

4.

Find $\frac{d}{dx}\left(\sin\left(x\right)x^2\right)$

a)

$2x\cos\left(x\right)-x^2\sin\left(x\right)$

b)

$2x\cos\left(x\right)$

c)

$2x\sin\left(x\right)$

d)

$x^2\cos\left(x\right)+2x\sin\left(x\right)$

5.

Find $\frac{d}{dx}\left(\frac{1}{x}\cos\left(x\right)\right)$

a)

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

b)

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

c)

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

d)

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

6.

THE ANSWER IS A WHOLE NUMBER, DO NOT WRITE DOWN ANY DECIMALS

Let $f$ be a function such that $f\left(-1\right)=3$ and $f'\left(-1\right)=5$

Let $g\left(x\right)=\frac{1}{x}$

And let $F\left(x\right)=f\left(x\right)\cdot g\left(x\right)$

Calculate $F'\left(-1\right)$

(a)

7.

Let $g\left(x\right)=x\cos\left(x\right)$

Find $g'\left(x\right)$

a)

$-\sin\left(x\right)$

b)

$\cos\left(x\right)+x\sin\left(x\right)$

c)

$\cos\left(x\right)-x\sin\left(x\right)$

d)

$-\cos\left(x\right)$

8.

Let $y=\sqrt[]{x}\cos\left(x\right)$

Find $\frac{dy}{dx}$

a)

$\frac{\cos\left(x\right)}{2\sqrt[]{x}}-\sqrt[]{x}\sin\left(x\right)$

b)

$-\frac{\sin\left(x\right)}{\sqrt[]{x}}$

c)

$-2\sqrt[]{x}\cos\left(x\right)-\sqrt[]{x}\sin\left(x\right)$

d)

$-\frac{1}{\sqrt[]{x}}+\sin\left(x\right)$

(M2W6.2) QUIZ - Differentiating; Product [QUIZIZZ]

Total questions: 8

Worksheet time: 1hrs 20mins

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