Question

Find the derivatives of the following functions

1. Y=3X42X-5
2. Y=5X34X+3
3. Y=U3+3U and U=-X2+10X
4. Y=(2X3+5)2
5. Y=4X5+2X3-X+ZX2-PX+50​

Answer 1

Answer

Let f(x)=(5x

3

+3x−1)(x−1)

Thus using product rule of differentiation,

f

′

(x)=(5x

3

+3x−1)

dx

d

(x−1)+(x−1)

dx

d

(5x

3

+3x−1)

=(5x

3

+3x−1)(1)+(x−1)(5.3x

2

+3−0)

=(5x

3

+3x−1)+(x−1)(15x

2

+3)

=5x

3

+3x−1+15x

3

+3x−15x

2

−3

=20x

3

−15x

2

+6x−4