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Popular >

derivative of y=(5x+1)^3(x-4)

Solution

derivative of

y = (5 x + 1)^{3} (x - 4)

Solution

15 (5 x + 1)^{2} (x - 4) + (5 x + 1)^{3}

Solution steps

\frac{d}{d x} ((5 x + 1)^{3} (x - 4))

Apply the Product Rule:

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

f = (5 x + 1)^{3}, g = x - 4

= \frac{d}{d x} ((5 x + 1)^{3}) (x - 4) + \frac{d}{d x} (x - 4) (5 x + 1)^{3}

\frac{d}{d x} ((5 x + 1)^{3}) = 15 (5 x + 1)^{2}

\frac{d}{d x} (x - 4) = 1

= 15 (5 x + 1)^{2} (x - 4) + 1 \cdot (5 x + 1)^{3}

Simplify

= 15 (5 x + 1)^{2} (x - 4) + (5 x + 1)^{3}

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Frequently Asked Questions (FAQ)

What is the derivative of y=(5x+1)^3(x-4) ?
The derivative of y=(5x+1)^3(x-4) is 15(5x+1)^2(x-4)+(5x+1)^3
What is the first derivative of y=(5x+1)^3(x-4) ?
The first derivative of y=(5x+1)^3(x-4) is 15(5x+1)^2(x-4)+(5x+1)^3