Question

evaluate d/dx(x8+x1/8)?

Answer 1

Answer:

d/dx( x^8 + x^1/8)

=> 8x^7 + 1/8x^(1/8-1)

=> 8x^7 + 1/8x^-7/8

Answer 2

Given,

Equation: x8+x1/8

To Find,

d/dx(x8+x1/8)

Solution,

We have to find a derivative of the given equation that is,

Derivative = $\frac{d}{dx} x^8+x^{1/8}$

By differentiating using the power rule   $\frac{d}{dx} x^n = n x^{n - 1}$  we get,

$\frac{d}{dx} x^8+x^{1/8} = 8 x^{8 - 1} + 1/8(x)^{1/8 -1}$

$\frac{d}{dx} x^8+x^{1/8} = 8 x^{7} + 1/8(x)^{1/8 -8/8}$

$\frac{d}{dx} x^8+x^{1/8} = 8 x^{7} + 1/8(x)^{-7/8}$

$\frac{d}{dx} x^8+x^{1/8} = 8 x^{7} + \frac{1}{8(x)^7/8}$

Hence, the answer is $8 x^{7} + \frac{1}{8(x)^7/8}$