What is the derivative of (x^2+1^{ln(x)}) ?

The derivative of (x^2+1^{ln(x)}) is x^{ln(x^2+1)}((ln(x^2+1))/x+(2xln(x))/(x^2+1))

What is the first derivative of (x^2+1^{ln(x)}) ?

The first derivative of (x^2+1^{ln(x)}) is x^{ln(x^2+1)}((ln(x^2+1))/x+(2xln(x))/(x^2+1))

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

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

(x^{2} + 1)^{l n (x)} = e^{l n (x) l n (x^{2} + 1)}

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

Apply the chain rule:

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

= e^{l n (x) l n (x^{2} + 1)} \frac{d}{d x} (ln (x) ln (x^{2} + 1))

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

= e^{l n (x) l n (x^{2} + 1)} (\frac{ln ( x ^{2} + 1 )}{x} + \frac{2 x ln ( x )}{x ^{2} + 1})

e^{l n (x) l n (x^{2} + 1)} = x^{l n (x^{2} + 1)}

= x^{l n (x^{2} + 1)} (\frac{ln ( x ^{2} + 1 )}{x} + \frac{2 x ln ( x )}{x ^{2} + 1})

i = 1 \sum \infty 4 (2)^{i - 1}

\int \frac{ln ( x ) - 2}{x ln ( x ) ( ln ( x ) - 1 )} d x

\int sin (x) ln (x) cos (x) d x

e^{m t}

\int \frac{x}{5 + 4 x} d x

What is the derivative of (x^2+1^{ln(x)}) ?
The derivative of (x^2+1^{ln(x)}) is x^{ln(x^2+1)}((ln(x^2+1))/x+(2xln(x))/(x^2+1))
What is the first derivative of (x^2+1^{ln(x)}) ?
The first derivative of (x^2+1^{ln(x)}) is x^{ln(x^2+1)}((ln(x^2+1))/x+(2xln(x))/(x^2+1))