Free Printable Differentiation

1.

find\ the\ derivative\ of\ \sin\left(x^2\ +5\right)

a)

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

b)

cos(2x)

c)

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

d)

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

2.

derivative of cos(sinx)

a)

-sin(sinx)

b)

-cosx.sin(sinx)

c)

-sin(cosx)

d)

cosx. sin(sinx)

3.

derivative of sec(tan√x)

a)

sec(tan√x)tan(tan√x)sec²√x.(1/2√x)

b)

sec(tan√x)tan(tan√x)sec²√x

c)

sec(tan√x)tan²(tan√x)sec²√x

d)

sec²(tan√x)

4.

derivative of 5^tanx

a)

5^tanx. sec²x

b)

tanx. log5

c)

5^tanx. sec²x. log5

d)

5^{secx. tanx}. log5

5.

derivative of sec^-1x

a)

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

b)

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

c)

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

d)

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

6.

derivative of cos^-1(2x)

a)

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

b)

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

c)

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

d)

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

7.

derivative of e^tanx

a)

e^tanxsec²x

b)

e^tanxsecx. tanx

c)

e^tanxlog secx

d)

None of these

8.

derivative of tan^-1x

a)

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

b)

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

c)

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

d)

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

9.

$derivative\ of\ \operatorname{cosec}\left(x^3\right)$ =

a)

$-3x^2\operatorname{cosec}(x^3)\cot(x^3)$

b)

$3x^2\operatorname{cosec}(x^3)\cot(x^3)$

c)

$-3x^2\operatorname{cosec}(3x^2)\cot(3x^2)$

d)

None of these

10.

$derivative\ of\ \left(x\ +4\right)^{\frac{3}{4}}$

a)

$\frac{6x}{4\left(x^2+4\right)^{\frac{1}{4}}}$

b)

$\frac{3}{4\left(x+4\right)^{\frac{1}{4}}}$

c)

$\frac{3}{4\left(x+4\right)^{\frac{7}{4}}}$

d)

none of these

Differentiation

Total questions: 10

Worksheet time: 5mins

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