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Popular Calculus >

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

Solution

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

Solution

5 x^{4} + 6 x^{2} + 2 x

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x (x^{3} + 1) + 3 x^{2} (x^{2} + 2) : 5 x^{4} + 6 x^{2} + 2 x

= 5 x^{4} + 6 x^{2} + 2 x

Graph

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\frac{d}{d x} (ln (x + y - 1))

x^2((dy)/(dx))=y-yx

x^{2} (\frac{d y}{d x}) = y - y x

derivative of y=(x+2)^2-3

d er i v a t i v e y = (x + 2)^{2} - 3

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\int (3 x^{2} + ln (x)) d x

integral from-5 to 5 of y/(sqrt(25-y^2))

\int_{- 5}^{5} \frac{y}{25 - y ^{2}} d y

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+2(x^3+1)) ?
The derivative of (x^2+2(x^3+1)) is 5x^4+6x^2+2x
What is the first derivative of (x^2+2(x^3+1)) ?
The first derivative of (x^2+2(x^3+1)) is 5x^4+6x^2+2x