What is the derivative of sqrt(65-25sin^2(x)) ?

The derivative of sqrt(65-25sin^2(x)) is -(25sin(2x))/(2sqrt(65-25sin^2(x)))

What is the first derivative of sqrt(65-25sin^2(x)) ?

The first derivative of sqrt(65-25sin^2(x)) is -(25sin(2x))/(2sqrt(65-25sin^2(x)))

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\frac{d}{d x} (65 - 25 sin^{2} (x))

- \frac{25 sin ( 2 x )}{2 65 - 25 sin ^{2} ( x )}

Solution steps

\frac{d}{d x} (65 - 25 sin^{2} (x))

Apply the chain rule:

\frac{1}{2 65 - 25 sin ^{2} ( x )} \frac{d}{d x} (65 - 25 sin^{2} (x))

= \frac{1}{2 65 - 25 sin ^{2} ( x )} \frac{d}{d x} (65 - 25 sin^{2} (x))

\frac{d}{d x} (65 - 25 sin^{2} (x)) = - 25 sin (2 x)

= \frac{1}{2 65 - 25 sin ^{2} ( x )} (- 25 sin (2 x))

Simplify

\frac{1}{2 65 - 25 sin ^{2} ( x )} (- 25 sin (2 x)) : - \frac{25 sin ( 2 x )}{2 65 - 25 sin ^{2} ( x )}

= - \frac{25 sin ( 2 x )}{2 65 - 25 sin ^{2} ( x )}

\int x^{2} (x^{3} + 5)^{6} d x

x \to 7 - lim (\frac{x}{x + 7})

\frac{d}{d x} (e^{3 x} (x^{2} + y^{2}))

\int \frac{1}{5 - 2 x + x ^{2}} d x

x \to + 0 - lim (\frac{1}{x} \cdot + e^{\frac{1}{x}})

What is the derivative of sqrt(65-25sin^2(x)) ?
The derivative of sqrt(65-25sin^2(x)) is -(25sin(2x))/(2sqrt(65-25sin^2(x)))
What is the first derivative of sqrt(65-25sin^2(x)) ?
The first derivative of sqrt(65-25sin^2(x)) is -(25sin(2x))/(2sqrt(65-25sin^2(x)))