What is the derivative of y=(x^5+1)^8 ?

The derivative of y=(x^5+1)^8 is 40x^4(x^5+1)^7

What is the first derivative of y=(x^5+1)^8 ?

The first derivative of y=(x^5+1)^8 is 40x^4(x^5+1)^7

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derivative of

y = (x^{5} + 1)^{8}

40 x^{4} (x^{5} + 1)^{7}

Solution steps

\frac{d}{d x} ((x^{5} + 1)^{8})

Apply the chain rule:

8 (x^{5} + 1)^{7} \frac{d}{d x} (x^{5} + 1)

= 8 (x^{5} + 1)^{7} \frac{d}{d x} (x^{5} + 1)

\frac{d}{d x} (x^{5} + 1) = 5 x^{4}

= 8 (x^{5} + 1)^{7} \cdot 5 x^{4}

Simplify

= 40 x^{4} (x^{5} + 1)^{7}

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What is the derivative of y=(x^5+1)^8 ?
The derivative of y=(x^5+1)^8 is 40x^4(x^5+1)^7
What is the first derivative of y=(x^5+1)^8 ?
The first derivative of y=(x^5+1)^8 is 40x^4(x^5+1)^7