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Popular >

derivative of (4x^2+5(5x-3))

Solution

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

Solution

60 x^{2} - 24 x + 25

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (4 x^{2} + 5) = 8 x

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

= 8 x (5 x - 3) + 5 (4 x^{2} + 5)

Simplify

8 x (5 x - 3) + 5 (4 x^{2} + 5) : 60 x^{2} - 24 x + 25

= 60 x^{2} - 24 x + 25

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Frequently Asked Questions (FAQ)

What is the derivative of (4x^2+5(5x-3)) ?
The derivative of (4x^2+5(5x-3)) is 60x^2-24x+25
What is the first derivative of (4x^2+5(5x-3)) ?
The first derivative of (4x^2+5(5x-3)) is 60x^2-24x+25