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Popular >

derivative of f(x)=(x^3+7x^2+5)^5

Solution

derivative of

f (x) = (x^{3} + 7 x^{2} + 5)^{5}

Solution

5 (x^{3} + 7 x^{2} + 5)^{4} (3 x^{2} + 14 x)

Solution steps

\frac{d}{d x} ((x^{3} + 7 x^{2} + 5)^{5})

Apply the chain rule:

5 (x^{3} + 7 x^{2} + 5)^{4} \frac{d}{d x} (x^{3} + 7 x^{2} + 5)

= 5 (x^{3} + 7 x^{2} + 5)^{4} \frac{d}{d x} (x^{3} + 7 x^{2} + 5)

\frac{d}{d x} (x^{3} + 7 x^{2} + 5) = 3 x^{2} + 14 x

= 5 (x^{3} + 7 x^{2} + 5)^{4} (3 x^{2} + 14 x)

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^3+7x^2+5)^5 ?
The derivative of f(x)=(x^3+7x^2+5)^5 is 5(x^3+7x^2+5)^4(3x^2+14x)
What is the first derivative of f(x)=(x^3+7x^2+5)^5 ?
The first derivative of f(x)=(x^3+7x^2+5)^5 is 5(x^3+7x^2+5)^4(3x^2+14x)