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Popular >

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

Solution

derivative of

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

Solution

135 x^{2} - 48 x - 28

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((3 x - 2)^{2}) = 6 (3 x - 2)

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

= 6 (3 x - 2) (5 x + 4) + 5 (3 x - 2)^{2}

Simplify

6 (3 x - 2) (5 x + 4) + 5 (3 x - 2)^{2} : 135 x^{2} - 48 x - 28

= 135 x^{2} - 48 x - 28

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Frequently Asked Questions (FAQ)

What is the derivative of y=(3x-2)^2(5x+4) ?
The derivative of y=(3x-2)^2(5x+4) is 135x^2-48x-28
What is the first derivative of y=(3x-2)^2(5x+4) ?
The first derivative of y=(3x-2)^2(5x+4) is 135x^2-48x-28