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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Popular Examples

derivative of arctan((x+1/(x-1)))

\frac{d}{d x} (arctan (\frac{x + 1}{x - 1}))

integral of 1/((x+1)^3(x+2))

\int \frac{1}{( x + 1 ) ^{3} ( x + 2 )} d x

derivative of f(x)=(2x-2)^4(x^2+x+1)^5 derivative of

f (x) = (2 x - 2)^{4} (x^{2} + x + 1)^{5}

(\partial)/(\partial x)(5ye^x)

\frac{\partial}{\partial x} (5 y e^{x})

tangent of y=6sqrt(x),(1,6)tangent of

y = 6 x, (1, 6)

Frequently Asked Questions (FAQ)

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