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Popular >

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

Popular Examples

d/(dt)(0.0225te^{-0.0467t})

\frac{d}{d t} (0.0225 t e^{- 0.0467 t})

integral of x/(sqrt(9-64x^2))

\int \frac{x}{9 - 64 x ^{2}} d x

integral from 0 to 16 of sqrt(1+3x)

\int_{0}^{16} 1 + 3 x d x

derivative of ln(x+y-1)

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

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

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

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