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Popular >

derivative of (x+1(2x+5)^4)

Solution

\frac{d}{d x} ((x + 1) (2 x + 5)^{4})

Solution

(2 x + 5)^{4} + 8 (2 x + 5)^{3} (x + 1)

Solution steps

\frac{d}{d x} ((x + 1) (2 x + 5)^{4})

Apply the Product Rule:

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

f = x + 1, g = (2 x + 5)^{4}

= \frac{d}{d x} (x + 1) (2 x + 5)^{4} + \frac{d}{d x} ((2 x + 5)^{4}) (x + 1)

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

\frac{d}{d x} ((2 x + 5)^{4}) = 8 (2 x + 5)^{3}

= 1 \cdot (2 x + 5)^{4} + 8 (2 x + 5)^{3} (x + 1)

Simplify

= (2 x + 5)^{4} + 8 (2 x + 5)^{3} (x + 1)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x+1(2x+5)^4) ?
The derivative of (x+1(2x+5)^4) is (2x+5)^4+8(2x+5)^3(x+1)
What is the first derivative of (x+1(2x+5)^4) ?
The first derivative of (x+1(2x+5)^4) is (2x+5)^4+8(2x+5)^3(x+1)