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

The derivative of (2x^2+5(5x-3)) is 30x^2-12x+25

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

The first derivative of (2x^2+5(5x-3)) is 30x^2-12x+25

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

30 x^{2} - 12 x + 25

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

4 x (5 x - 3) + 5 (2 x^{2} + 5) : 30 x^{2} - 12 x + 25

= 30 x^{2} - 12 x + 25

What is the derivative of (2x^2+5(5x-3)) ?
The derivative of (2x^2+5(5x-3)) is 30x^2-12x+25
What is the first derivative of (2x^2+5(5x-3)) ?
The first derivative of (2x^2+5(5x-3)) is 30x^2-12x+25