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

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

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

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

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derivative of

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}

x \to 2 lim (\frac{3 x}{x - 2})

\int sin^{4} (θ) d θ

\int \frac{3}{4} sec (x) tan (x) d x

tan (2 x + 3)

x \to 0 lim (3 - 7 x - 5 x^{2})

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