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

The derivative of (5x^2+3)(2x-5) is 30x^2-50x+6

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

The first derivative of (5x^2+3)(2x-5) is 30x^2-50x+6

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derivative of

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

30 x^{2} - 50 x + 6

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (2 x - 5) = 2

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

Simplify

10 x (2 x - 5) + 2 (5 x^{2} + 3) : 30 x^{2} - 50 x + 6

= 30 x^{2} - 50 x + 6

What is the derivative of (5x^2+3)(2x-5) ?
The derivative of (5x^2+3)(2x-5) is 30x^2-50x+6
What is the first derivative of (5x^2+3)(2x-5) ?
The first derivative of (5x^2+3)(2x-5) is 30x^2-50x+6