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Popular >

derivative of y=(2x+1)(x+5)^3

Solution

derivative of

y = (2 x + 1) (x + 5)^{3}

Solution

2 (x + 5)^{3} + 3 (x + 5)^{2} (2 x + 1)

Solution steps

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

Apply the Product Rule:

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

f = 2 x + 1, g = (x + 5)^{3}

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

\frac{d}{d x} (2 x + 1) = 2

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

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

Graph

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Frequently Asked Questions (FAQ)

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