What is the derivative of sin(xln(x^2+1)) ?

The derivative of sin(xln(x^2+1)) is cos(x)ln(x^2+1)+(2xsin(x))/(x^2+1)

What is the first derivative of sin(xln(x^2+1)) ?

The first derivative of sin(xln(x^2+1)) is cos(x)ln(x^2+1)+(2xsin(x))/(x^2+1)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = ln (x^{2} + 1)

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

\frac{d}{d x} (sin (x)) = cos (x)

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{d y}{d x}, tan (x - y) = \frac{y}{1 - x ^{2}}

\int cot (42 x) d x

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

\frac{d}{d x} (3^{x^{3} - x + 1})

\frac{d}{d x} (arcsec (\frac{x}{a}))

What is the derivative of sin(xln(x^2+1)) ?
The derivative of sin(xln(x^2+1)) is cos(x)ln(x^2+1)+(2xsin(x))/(x^2+1)
What is the first derivative of sin(xln(x^2+1)) ?
The first derivative of sin(xln(x^2+1)) is cos(x)ln(x^2+1)+(2xsin(x))/(x^2+1)