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Popular >

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

Solution

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

Solution

sec (x) tan (x)

Solution steps

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

Simplify

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

= \frac{d}{d x} (sec^{2} (x))

Apply the chain rule:

\frac{1}{2 sec ^{2} ( x )} \frac{d}{d x} (sec^{2} (x))

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

\frac{d}{d x} (sec^{2} (x)) = 2 sec^{2} (x) tan (x)

= \frac{1}{2 sec ^{2} ( x )} \cdot 2 sec^{2} (x) tan (x)

Simplify

\frac{1}{2 sec ^{2} ( x )} \cdot 2 sec^{2} (x) tan (x) : sec (x) tan (x)

= sec (x) tan (x)

Popular Examples

integral of 7/(1-x^2)

\int \frac{7}{1 - x ^{2}} d x

derivative of (2t-1)(5t-5)^{-1}derivative of

(2 t - 1) (5 t - 5)^{- 1}

limit as x approaches 2 of 1/((x-2)^3)

x \to 2 lim (\frac{1}{( x - 2 ) ^{3}})

y^{''}-y^'-2y=-2t+8t^2

y^{^{''}} - y^{^{'}} - 2 y = - 2 t + 8 t^{2}

inverse oflaplace 4/((s-1)^3)inverse laplace

\frac{4}{( s - 1 ) ^{3}}

Frequently Asked Questions (FAQ)

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