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Popular >

derivative of sqrt(1-sin^2(x))

Solution

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

Solution

- \frac{sin ( 2 x )}{2 cos ( x )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{sin ( 2 x )}{2 cos ( x )}

Popular Examples

integral from-3 to 5 of 6-y-((y-3)^2)/4

\int_{- 3}^{5} 6 - y - \frac{( y - 3 ) ^{2}}{4} d y

derivative of f(x)=7tan^3(x)derivative of

f (x) = 7 tan^{3} (x)

derivative of 16^x derivative of

1 6^{x}

integral of+(16)/((64x^2+1)^2)

\int + \frac{16}{( 64 x ^{2} + 1 ) ^{2}} d x

integral from-infinity to 0 of 1/(4-5x)

\int_{- \infty}^{0} \frac{1}{4 - 5 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(1-sin^2(x)) ?
The derivative of sqrt(1-sin^2(x)) is -(sin(2x))/(2cos(x))
What is the first derivative of sqrt(1-sin^2(x)) ?
The first derivative of sqrt(1-sin^2(x)) is -(sin(2x))/(2cos(x))