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Popular >

derivative of f(x)=(8x^3+2x^2)^4

Solution

derivative of

f (x) = (8 x^{3} + 2 x^{2})^{4}

Solution

4 (8 x^{3} + 2 x^{2})^{3} (24 x^{2} + 4 x)

Solution steps

\frac{d}{d x} ((8 x^{3} + 2 x^{2})^{4})

Apply the chain rule:

4 (8 x^{3} + 2 x^{2})^{3} \frac{d}{d x} (8 x^{3} + 2 x^{2})

= 4 (8 x^{3} + 2 x^{2})^{3} \frac{d}{d x} (8 x^{3} + 2 x^{2})

\frac{d}{d x} (8 x^{3} + 2 x^{2}) = 24 x^{2} + 4 x

= 4 (8 x^{3} + 2 x^{2})^{3} (24 x^{2} + 4 x)

Popular Examples

derivative of (1+9x^2(x-x^2))

\frac{d}{d x} ((1 + 9 x^{2}) (x - x^{2}))

derivative of arctan(arcsin(sqrt(x)))

\frac{d}{d x} (arctan (arcsin (x)))

integral of 3y^5sqrt(y^3+1)

\int 3 y^{5} y^{3} + 1 d y

limit as x approaches-1 of x+2x^4

x \to - 1 lim (x + 2 x^{4})

derivative of axe^{-x}

\frac{d}{d x} (a x e^{- x})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(8x^3+2x^2)^4 ?
The derivative of f(x)=(8x^3+2x^2)^4 is 4(8x^3+2x^2)^3(24x^2+4x)
What is the first derivative of f(x)=(8x^3+2x^2)^4 ?
The first derivative of f(x)=(8x^3+2x^2)^4 is 4(8x^3+2x^2)^3(24x^2+4x)