What is the derivative of (8x^2+3(3-x^2+7x)) ?

The derivative of (8x^2+3(3-x^2+7x)) is -32x^3+168x^2+42x+21

What is the first derivative of (8x^2+3(3-x^2+7x)) ?

The first derivative of (8x^2+3(3-x^2+7x)) is -32x^3+168x^2+42x+21

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\frac{d}{d x} ((8 x^{2} + 3) (3 - x^{2} + 7 x))

- 32 x^{3} + 168 x^{2} + 42 x + 21

Solution steps

\frac{d}{d x} ((8 x^{2} + 3) (3 - x^{2} + 7 x))

Apply the Product Rule:

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

f = 8 x^{2} + 3, g = 3 - x^{2} + 7 x

= \frac{d}{d x} (8 x^{2} + 3) (3 - x^{2} + 7 x) + \frac{d}{d x} (3 - x^{2} + 7 x) (8 x^{2} + 3)

\frac{d}{d x} (8 x^{2} + 3) = 16 x

\frac{d}{d x} (3 - x^{2} + 7 x) = - 2 x + 7

= 16 x (3 - x^{2} + 7 x) + (- 2 x + 7) (8 x^{2} + 3)

Simplify

16 x (3 - x^{2} + 7 x) + (- 2 x + 7) (8 x^{2} + 3) : - 32 x^{3} + 168 x^{2} + 42 x + 21

= - 32 x^{3} + 168 x^{2} + 42 x + 21

\frac{e ^{- s}}{s - 2}

\frac{d}{d x} (\frac{1}{x ^{2} ln ( x )})

f (x) = 7 x + 11, at x = 2

\frac{d y}{d x} = \frac{cos ( 8 x )}{e ^{8 y}}

g (x) = (5 - x)^{2} (2 x - 1)^{5}

What is the derivative of (8x^2+3(3-x^2+7x)) ?
The derivative of (8x^2+3(3-x^2+7x)) is -32x^3+168x^2+42x+21
What is the first derivative of (8x^2+3(3-x^2+7x)) ?
The first derivative of (8x^2+3(3-x^2+7x)) is -32x^3+168x^2+42x+21