Question

find derevative of x^8+x​

Answer 1

The solution is given in the above attachment.

Answer 2

Answer:

$\Large\boxed{\mathsf{8x^7+1}}}$

Step-by-step explanation:

QUESTION:

Find derivative of x⁸+x.

TO FIND:

The derivative of x⁸+x.

You can also isolate it on one side of the equation.

SOLUTIONS:

First, use apply the sum & difference rule.

$\Large\boxed{\mathsf{SUM \quad DIFFERENCE \quad RULE}}$

$\displaystyle \mathsf{(F\pm G)'=F' \pm G'}$

$\displaystyle \mathsf{\frac{d}{dx}\left(x^8\right)+\frac{d}{dx}\left(x\right)}}}$

Power rule.

$\Large\boxed{\mathsf{POWER \quad RULES}}$

$\displaystyle \mathsf{\frac{d}{dx}\left(x^a\right)=a* x^{a-1}}}}$

$\displaystyle \mathsf{8x^{8-1}}$

Solve.

Subtract the numbers from left to right.

$\displaystyle \mathsf{8-1=7}$

$\displaystyle \mathsf{8x^7}}}$

Common derivative.

$\displaystyle \mathsf{\frac{d}{dx}\left(x\right)}}}$

$\displaystyle \mathsf{\frac{d}{dx}(x)=1 }$

$\displaystyle \mathsf{\Rightarrow8x^7+1}}$

$\Large\boxed{\mathsf{8x^7+1}}$

The correct answer is 8x⁷+1.