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Popular >

derivative of x^2ln(4x+3)

Solution

derivative of

x^{2} ln (4 x + 3)

Solution

2 x ln (4 x + 3) + \frac{4 x ^{2}}{4 x + 3}

Solution steps

\frac{d}{d x} (x^{2} ln (4 x + 3))

Apply the Product Rule:

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

f = x^{2}, g = ln (4 x + 3)

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

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

\frac{d}{d x} (ln (4 x + 3)) = \frac{4}{4 x + 3}

= 2 x ln (4 x + 3) + \frac{4}{4 x + 3} x^{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x ln (4 x + 3) + \frac{4 x ^{2}}{4 x + 3}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of x^2ln(4x+3) ?
The derivative of x^2ln(4x+3) is 2xln(4x+3)+(4x^2)/(4x+3)
What is the first derivative of x^2ln(4x+3) ?
The first derivative of x^2ln(4x+3) is 2xln(4x+3)+(4x^2)/(4x+3)