What is the derivative of 9ln(sqrt(1+x^2)) ?

The derivative of 9ln(sqrt(1+x^2)) is (9x)/(1+x^2)

What is the first derivative of 9ln(sqrt(1+x^2)) ?

The first derivative of 9ln(sqrt(1+x^2)) is (9x)/(1+x^2)

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\frac{d}{d x} (9 ln (1 + x^{2}))

\frac{9 x}{1 + x ^{2}}

Solution steps

\frac{d}{d x} (9 ln (1 + x^{2}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (ln (1 + x^{2}))

Apply the chain rule:

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

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

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

= 9 \cdot \frac{1}{1 + x ^{2}} \cdot \frac{x}{1 + x ^{2}}

Simplify

9 \cdot \frac{1}{1 + x ^{2}} \cdot \frac{x}{1 + x ^{2}} : \frac{9 x}{1 + x ^{2}}

= \frac{9 x}{1 + x ^{2}}

x \to 6 lim (c x^{2} + 7 x)

\int z^{11} d z

\int (cos (x))^{2} (tan (x))^{3} d x

\int \frac{1}{x ( 1000 - x )} d x

{\frac{1}{s ( s - 1 )}}

What is the derivative of 9ln(sqrt(1+x^2)) ?
The derivative of 9ln(sqrt(1+x^2)) is (9x)/(1+x^2)
What is the first derivative of 9ln(sqrt(1+x^2)) ?
The first derivative of 9ln(sqrt(1+x^2)) is (9x)/(1+x^2)