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Popular >

derivative of ln(axsqrt(a+x))

Solution

\frac{d}{d x} (ln (a x a + x))

Solution

\frac{3 x + 2 a}{2 x ( a + x )}

Solution steps

\frac{d}{d x} (ln (a x a + x))

Apply the chain rule:

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

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

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

= \frac{1}{a x a + x} \cdot \frac{a ( 3 x + 2 a )}{2 a + x}

Simplify

\frac{1}{a x a + x} \cdot \frac{a ( 3 x + 2 a )}{2 a + x} : \frac{3 x + 2 a}{2 x ( a + x )}

= \frac{3 x + 2 a}{2 x ( a + x )}

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\int \frac{1}{( x ^{2} - 49 ) ^{\frac{3}{2}}} d x

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t \to 0 lim (\frac{6}{1 + t})

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(axsqrt(a+x)) ?
The derivative of ln(axsqrt(a+x)) is (3x+2a)/(2x(a+x))
What is the first derivative of ln(axsqrt(a+x)) ?
The first derivative of ln(axsqrt(a+x)) is (3x+2a)/(2x(a+x))