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2.2 Basic Differentiation Rules

Total questions: 10

Worksheet time: 14mins

Name
Class
Date
1.

Differentiate with respect to x.

a)
b)
c)
d)
2.

Differentiate with respect to x. f(x)=xf\left(x\right)=x  

a)

 f(x)=1f'\left(x\right)=1  

b)

 f(x)=0f'\left(x\right)=0  

c)

 f(x)=10xf'\left(x\right)=10x  

d)

 f(x)=xf'\left(x\right)=x  

3.

Differentiate with respect to x. y=1x3y=\frac{1}{x^3}  


a)

 yx=1x4\frac{\partial y}{\partial x}=\frac{1}{x^4}  

b)

 yx=3x\frac{\partial y}{\partial x}=-3x  

c)

 yx=3x3\frac{\partial y}{\partial x}=-\frac{3}{x^3}  

d)

 yx=3x4\frac{\partial y}{\partial x}=-\frac{3}{x^4}  

4.

Differentiate with respect to x.

a)
b)
c)
d)
5.

Differentiate with respect to x.

a)
b)
c)
d)
6.

Differentiate with respect to x.

a)
b)
c)
d)
7.

Differentiate with respect to x.  f(x)=5x5+sinxf\left(x\right)=5x^5+\sin x  

a)

 f(x)=20x4+cosxf'\left(x\right)=20x^4+\cos x  

b)

 f(x)=25x4+cosxf'\left(x\right)=25x^4+\cos x  

c)

 f(x)=25x4sinxf'\left(x\right)=25x^4-\sin x  

d)

 f(x)=10x4+cosxf'\left(x\right)=10x^4+\cos x  

8.

Differentiate with respect to x.  f(x)=4x23+cosxf\left(x\right)=4x^{\frac{2}{3}}+\cos x  

a)

 f(x)=83x13+sinxf'\left(x\right)=\frac{8}{3x^{\frac{1}{3}}}+\sin x  

b)

 f(x)=83x13sinxf'\left(x\right)=\frac{8}{3x^{\frac{1}{3}}}-\sin x  

c)

 f(x)=83x13sinxf'\left(x\right)=\frac{8}{3}x^{\frac{1}{3}}-\sin x  

d)

 f(x)=6x13+sinxf'\left(x\right)=\frac{6}{x^{\frac{1}{3}}}+\sin x  

9.

Differentiate with respect to x.  f(x)=10x10sinxcosxf\left(x\right)=10x^{10}-\sin x-\cos x  

a)

 f(x)=100x9+cosxsinxf'\left(x\right)=100x^9+\cos x-\sin x  

b)

 f(x)=20x9+cosxsinxf'\left(x\right)=20x^9+\cos x-\sin x  

c)

 f(x)=20x9cosx+sinxf'\left(x\right)=20x^9-\cos x+\sin x  

d)

 f(x)=100x9cosx+sinxf'\left(x\right)=100x^9-\cos x+\sin x  

10.

Differentiate with respect to x. f(x)=14x34cosx+14f\left(x\right)=\frac{1}{4}x^{\frac{3}{4}}-\cos x+14  

a)

 f(x)=316x14+sinxf'\left(x\right)=\frac{3}{16x^{\frac{1}{4}}}+\sin x  

b)

 f(x)=316x14+sinx+1f'\left(x\right)=\frac{3}{16x^{\frac{1}{4}}}+\sin x+1  

c)

 f(x)=3x1416+sinxf'\left(x\right)=\frac{3x^{\frac{1}{4}}}{16}+\sin x  

d)

 f(x)=316x14sinxf'\left(x\right)=\frac{3}{16x^{\frac{1}{4}}}-\sin x