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Popular Calculus >

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

Solution

derivative of

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

Solution

2 x (2 x + 3)^{5} + 10 (2 x + 3)^{4} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} ((2 x + 3)^{5}) = 10 (2 x + 3)^{4}

= 2 x (2 x + 3)^{5} + 10 (2 x + 3)^{4} x^{2}

Graph

Popular Examples

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\frac{d}{d x} (tan (5 x^{4}))

Frequently Asked Questions (FAQ)

What is the derivative of y=x^2(2x+3)^5 ?
The derivative of y=x^2(2x+3)^5 is 2x(2x+3)^5+10(2x+3)^4x^2
What is the first derivative of y=x^2(2x+3)^5 ?
The first derivative of y=x^2(2x+3)^5 is 2x(2x+3)^5+10(2x+3)^4x^2