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Popular >

derivative of ln(sin(x^2+1))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of 4x^6-2x^3+7x-4

\int 4 x^{6} - 2 x^{3} + 7 x - 4 d x

integral from 2 to 5 of 1/(x^2)

\int_{2}^{5} \frac{1}{x ^{2}} d x

integral from 0 to 2 of ((4x+3))/(x^4)

\int_{0}^{2} \frac{( 4 x + 3 )}{x ^{4}} d x

derivative of asin^3(x/3)

\frac{d}{d x} (a sin^{3} (\frac{x}{3}))

y^'+y/x =(e^x)/x

y^{^{'}} + \frac{y}{x} = \frac{e ^{x}}{x}

Frequently Asked Questions (FAQ)

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