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Popular >

derivative of f(x)=(5x^6+2x^3)^4

Solution

derivative of

f (x) = (5 x^{6} + 2 x^{3})^{4}

Solution

4 (5 x^{6} + 2 x^{3})^{3} (30 x^{5} + 6 x^{2})

Solution steps

\frac{d}{d x} ((5 x^{6} + 2 x^{3})^{4})

Apply the chain rule:

4 (5 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (5 x^{6} + 2 x^{3})

= 4 (5 x^{6} + 2 x^{3})^{3} \frac{d}{d x} (5 x^{6} + 2 x^{3})

\frac{d}{d x} (5 x^{6} + 2 x^{3}) = 30 x^{5} + 6 x^{2}

= 4 (5 x^{6} + 2 x^{3})^{3} (30 x^{5} + 6 x^{2})

Popular Examples

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\int \frac{1}{- x - 1} d x

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f^'(t)-f(t)=-7t,f(2)=-4

f^{^{'}} (t) - f (t) = - 7 t, f (2) = - 4

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(5x^6+2x^3)^4 ?
The derivative of f(x)=(5x^6+2x^3)^4 is 4(5x^6+2x^3)^3(30x^5+6x^2)
What is the first derivative of f(x)=(5x^6+2x^3)^4 ?
The first derivative of f(x)=(5x^6+2x^3)^4 is 4(5x^6+2x^3)^3(30x^5+6x^2)