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Popular >

derivative of y=ln(1+sin(sqrt(x)))

Solution

derivative of

y = ln (1 + sin (x))

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (sin(x))/(7+cos^2(x))

\int \frac{sin ( x )}{7 + cos ^{2} ( x )} d x

derivative of 4x^4-32x^3+89x^2-95x+29

\frac{d}{d x} (4 x^{4} - 32 x^{3} + 89 x^{2} - 95 x + 29)

limit as x approaches-5+of (x+4)/(x+5)

x \to - 5 + lim (\frac{x + 4}{x + 5})

integral from 0 to 2 of 4x-2x^2

\int_{0}^{2} 4 x - 2 x^{2} d x

laplacetransform t+sin(t)laplace transform

t + sin (t)

Frequently Asked Questions (FAQ)

What is the derivative of y=ln(1+sin(sqrt(x))) ?
The derivative of y=ln(1+sin(sqrt(x))) is (cos(sqrt(x)))/(2sqrt(x)(1+sin(\sqrt{x)))}
What is the first derivative of y=ln(1+sin(sqrt(x))) ?
The first derivative of y=ln(1+sin(sqrt(x))) is (cos(sqrt(x)))/(2sqrt(x)(1+sin(\sqrt{x)))}