What is the derivative of ln^2(sqrt(x^2+5x+8)) ?

The derivative of ln^2(sqrt(x^2+5x+8)) is (ln(x^2+5x+8)(2x+5))/(2(x^2+5x+8))

What is the first derivative of ln^2(sqrt(x^2+5x+8)) ?

The first derivative of ln^2(sqrt(x^2+5x+8)) is (ln(x^2+5x+8)(2x+5))/(2(x^2+5x+8))

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\frac{d}{d x} (ln^{2} (x^{2} + 5 x + 8))

\frac{ln ( x ^{2} + 5 x + 8 ) ( 2 x + 5 )}{2 ( x ^{2} + 5 x + 8 )}

Solution steps

\frac{d}{d x} (ln^{2} (x^{2} + 5 x + 8))

Apply the chain rule:

2 ln (x^{2} + 5 x + 8) \frac{d}{d x} (ln (x^{2} + 5 x + 8))

= 2 ln (x^{2} + 5 x + 8) \frac{d}{d x} (ln (x^{2} + 5 x + 8))

\frac{d}{d x} (ln (x^{2} + 5 x + 8)) = \frac{2 x + 5}{2 ( x ^{2} + 5 x + 8 )}

= 2 ln (x^{2} + 5 x + 8) \frac{2 x + 5}{2 ( x ^{2} + 5 x + 8 )}

Simplify

2 ln (x^{2} + 5 x + 8) \frac{2 x + 5}{2 ( x ^{2} + 5 x + 8 )} : \frac{ln ( x ^{2} + 5 x + 8 ) ( 2 x + 5 )}{2 ( x ^{2} + 5 x + 8 )}

= \frac{ln ( x ^{2} + 5 x + 8 ) ( 2 x + 5 )}{2 ( x ^{2} + 5 x + 8 )}

x \to 0 + lim (e^{(- \frac{1}{x})})

h (t) = t^{\frac{3}{4}} - 4 t^{\frac{1}{4}}

\frac{d}{d t} (\frac{2}{t})

\frac{1}{3} (16 + x^{2})^{3}

\int tan^{4} (x) sec^{8} (x) d x

What is the derivative of ln^2(sqrt(x^2+5x+8)) ?
The derivative of ln^2(sqrt(x^2+5x+8)) is (ln(x^2+5x+8)(2x+5))/(2(x^2+5x+8))
What is the first derivative of ln^2(sqrt(x^2+5x+8)) ?
The first derivative of ln^2(sqrt(x^2+5x+8)) is (ln(x^2+5x+8)(2x+5))/(2(x^2+5x+8))