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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int 25 - x^{2} (- 2 x) d x

x \to 1 + lim (\frac{1 - x}{x ^{2} - 1})

\int (2 x - 5)^{7} d x

\int \frac{18}{x ^{2} - x - 20} d x

\int (6 e^{x} + \frac{7}{x}) d x

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