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

The derivative of (3x-5)(x^2+4) is 9x^2-10x+12

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

The first derivative of (3x-5)(x^2+4) is 9x^2-10x+12

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derivative of

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

9 x^{2} - 10 x + 12

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (3 x - 5) = 3

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

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

Simplify

3 (x^{2} + 4) + 2 x (3 x - 5) : 9 x^{2} - 10 x + 12

= 9 x^{2} - 10 x + 12

What is the derivative of (3x-5)(x^2+4) ?
The derivative of (3x-5)(x^2+4) is 9x^2-10x+12
What is the first derivative of (3x-5)(x^2+4) ?
The first derivative of (3x-5)(x^2+4) is 9x^2-10x+12