What is the derivative of (x^3+1(2x^2+8x-5)) ?

The derivative of (x^3+1(2x^2+8x-5)) is 10x^4+32x^3-15x^2+4x+8

What is the first derivative of (x^3+1(2x^2+8x-5)) ?

The first derivative of (x^3+1(2x^2+8x-5)) is 10x^4+32x^3-15x^2+4x+8

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\frac{d}{d x} ((x^{3} + 1) (2 x^{2} + 8 x - 5))

10 x^{4} + 32 x^{3} - 15 x^{2} + 4 x + 8

Solution steps

\frac{d}{d x} ((x^{3} + 1) (2 x^{2} + 8 x - 5))

Apply the Product Rule:

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

f = x^{3} + 1, g = 2 x^{2} + 8 x - 5

= \frac{d}{d x} (x^{3} + 1) (2 x^{2} + 8 x - 5) + \frac{d}{d x} (2 x^{2} + 8 x - 5) (x^{3} + 1)

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

\frac{d}{d x} (2 x^{2} + 8 x - 5) = 4 x + 8

= 3 x^{2} (2 x^{2} + 8 x - 5) + (4 x + 8) (x^{3} + 1)

Simplify

3 x^{2} (2 x^{2} + 8 x - 5) + (4 x + 8) (x^{3} + 1) : 10 x^{4} + 32 x^{3} - 15 x^{2} + 4 x + 8

= 10 x^{4} + 32 x^{3} - 15 x^{2} + 4 x + 8

\int \frac{1}{1 + 2 x ^{2}} d x

\int (e^{2 x} + 1) d x

\int \frac{2 x + 4}{x ^{2} + 4 x + 8} d x

\int x + 2 d x

x d x + sin^{2} (x^{- 1} y) (y d x - x d y) = 0

What is the derivative of (x^3+1(2x^2+8x-5)) ?
The derivative of (x^3+1(2x^2+8x-5)) is 10x^4+32x^3-15x^2+4x+8
What is the first derivative of (x^3+1(2x^2+8x-5)) ?
The first derivative of (x^3+1(2x^2+8x-5)) is 10x^4+32x^3-15x^2+4x+8