What is the derivative of (5x^2+3(4x-3)) ?

The derivative of (5x^2+3(4x-3)) is 60x^2-30x+12

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

The first derivative of (5x^2+3(4x-3)) is 60x^2-30x+12

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\frac{d}{d x} ((5 x^{2} + 3) (4 x - 3))

60 x^{2} - 30 x + 12

Solution steps

\frac{d}{d x} ((5 x^{2} + 3) (4 x - 3))

Apply the Product Rule:

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

f = 5 x^{2} + 3, g = 4 x - 3

= \frac{d}{d x} (5 x^{2} + 3) (4 x - 3) + \frac{d}{d x} (4 x - 3) (5 x^{2} + 3)

\frac{d}{d x} (5 x^{2} + 3) = 10 x

\frac{d}{d x} (4 x - 3) = 4

= 10 x (4 x - 3) + 4 (5 x^{2} + 3)

Simplify

10 x (4 x - 3) + 4 (5 x^{2} + 3) : 60 x^{2} - 30 x + 12

= 60 x^{2} - 30 x + 12

\frac{d}{d x} (14 x e^{x})

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\int (x + 5) (x - 3) d x

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\int x^{6} (x + 4) d x

What is the derivative of (5x^2+3(4x-3)) ?
The derivative of (5x^2+3(4x-3)) is 60x^2-30x+12
What is the first derivative of (5x^2+3(4x-3)) ?
The first derivative of (5x^2+3(4x-3)) is 60x^2-30x+12