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Popular >

derivative of x(3x+2^5)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((3 x + 2)^{5}) = 15 (3 x + 2)^{4}

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

Simplify

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

Graph

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Frequently Asked Questions (FAQ)

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