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Popular Calculus >

derivative of (1+4x^3(1+2x^2))

Solution

\frac{d}{d x} ((1 + 4 x^{3}) (1 + 2 x^{2}))

Solution

40 x^{4} + 12 x^{2} + 4 x

Solution steps

\frac{d}{d x} ((1 + 4 x^{3}) (1 + 2 x^{2}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 + 4 x^{3}, g = 1 + 2 x^{2}

= \frac{d}{d x} (1 + 4 x^{3}) (1 + 2 x^{2}) + \frac{d}{d x} (1 + 2 x^{2}) (1 + 4 x^{3})

\frac{d}{d x} (1 + 4 x^{3}) = 12 x^{2}

\frac{d}{d x} (1 + 2 x^{2}) = 4 x

= 12 x^{2} (1 + 2 x^{2}) + 4 x (1 + 4 x^{3})

Simplify

12 x^{2} (1 + 2 x^{2}) + 4 x (1 + 4 x^{3}) : 40 x^{4} + 12 x^{2} + 4 x

= 40 x^{4} + 12 x^{2} + 4 x

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (1+4x^3(1+2x^2)) ?
The derivative of (1+4x^3(1+2x^2)) is 40x^4+12x^2+4x
What is the first derivative of (1+4x^3(1+2x^2)) ?
The first derivative of (1+4x^3(1+2x^2)) is 40x^4+12x^2+4x