What is the derivative of sqrt(4sin^2(x+9cos^2(x))) ?

The derivative of sqrt(4sin^2(x+9cos^2(x))) is -(5sin(2x))/(2sqrt(4sin^2(x)+9cos^2(x)))

What is the first derivative of sqrt(4sin^2(x+9cos^2(x))) ?

The first derivative of sqrt(4sin^2(x+9cos^2(x))) is -(5sin(2x))/(2sqrt(4sin^2(x)+9cos^2(x)))

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\frac{d}{d x} (4 sin^{2} (x) + 9 cos^{2} (x))

- \frac{5 sin ( 2 x )}{2 4 sin ^{2} ( x ) + 9 cos ^{2} ( x )}

Solution steps

\frac{d}{d x} (4 sin^{2} (x) + 9 cos^{2} (x))

Apply the chain rule:

\frac{1}{2 4 sin ^{2} ( x ) + 9 cos ^{2} ( x )} \frac{d}{d x} (4 sin^{2} (x) + 9 cos^{2} (x))

= \frac{1}{2 4 sin ^{2} ( x ) + 9 cos ^{2} ( x )} \frac{d}{d x} (4 sin^{2} (x) + 9 cos^{2} (x))

\frac{d}{d x} (4 sin^{2} (x) + 9 cos^{2} (x)) = - 5 sin (2 x)

= \frac{1}{2 4 sin ^{2} ( x ) + 9 cos ^{2} ( x )} (- 5 sin (2 x))

Simplify

\frac{1}{2 4 sin ^{2} ( x ) + 9 cos ^{2} ( x )} (- 5 sin (2 x)) : - \frac{5 sin ( 2 x )}{2 4 sin ^{2} ( x ) + 9 cos ^{2} ( x )}

= - \frac{5 sin ( 2 x )}{2 4 sin ^{2} ( x ) + 9 cos ^{2} ( x )}

What is the derivative of sqrt(4sin^2(x+9cos^2(x))) ?
The derivative of sqrt(4sin^2(x+9cos^2(x))) is -(5sin(2x))/(2sqrt(4sin^2(x)+9cos^2(x)))
What is the first derivative of sqrt(4sin^2(x+9cos^2(x))) ?
The first derivative of sqrt(4sin^2(x+9cos^2(x))) is -(5sin(2x))/(2sqrt(4sin^2(x)+9cos^2(x)))