What is the derivative of (2x^2+7(8x-4)) ?

The derivative of (2x^2+7(8x-4)) is 48x^2-16x+56

What is the first derivative of (2x^2+7(8x-4)) ?

The first derivative of (2x^2+7(8x-4)) is 48x^2-16x+56

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\frac{d}{d x} ((2 x^{2} + 7) (8 x - 4))

48 x^{2} - 16 x + 56

Solution steps

\frac{d}{d x} ((2 x^{2} + 7) (8 x - 4))

Apply the Product Rule:

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

f = 2 x^{2} + 7, g = 8 x - 4

= \frac{d}{d x} (2 x^{2} + 7) (8 x - 4) + \frac{d}{d x} (8 x - 4) (2 x^{2} + 7)

\frac{d}{d x} (2 x^{2} + 7) = 4 x

\frac{d}{d x} (8 x - 4) = 8

= 4 x (8 x - 4) + 8 (2 x^{2} + 7)

Simplify

4 x (8 x - 4) + 8 (2 x^{2} + 7) : 48 x^{2} - 16 x + 56

= 48 x^{2} - 16 x + 56

What is the derivative of (2x^2+7(8x-4)) ?
The derivative of (2x^2+7(8x-4)) is 48x^2-16x+56
What is the first derivative of (2x^2+7(8x-4)) ?
The first derivative of (2x^2+7(8x-4)) is 48x^2-16x+56