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Popular >

derivative of y=(2x^2+5)(4x-5)

Solution

derivative of

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

Solution

24 x^{2} - 20 x + 20

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (4 x - 5) = 4

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

Simplify

4 x (4 x - 5) + 4 (2 x^{2} + 5) : 24 x^{2} - 20 x + 20

= 24 x^{2} - 20 x + 20

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=(2x^2+5)(4x-5) ?
The derivative of y=(2x^2+5)(4x-5) is 24x^2-20x+20
What is the first derivative of y=(2x^2+5)(4x-5) ?
The first derivative of y=(2x^2+5)(4x-5) is 24x^2-20x+20