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Popular >

derivative of y=ln(x^2sqrt(x+1))

Solution

derivative of

y = ln (x^{2} x + 1)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{x ^{2} x + 1} \cdot \frac{5 x ^{2} + 4 x}{2 x + 1}

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of y=ln(x^2sqrt(x+1)) ?
The derivative of y=ln(x^2sqrt(x+1)) is (5x+4)/(2x(x+1))
What is the first derivative of y=ln(x^2sqrt(x+1)) ?
The first derivative of y=ln(x^2sqrt(x+1)) is (5x+4)/(2x(x+1))