What is the derivative of sqrt(3x-sin^2(4x)) ?

The derivative of sqrt(3x-sin^2(4x)) is (3-4sin(8x))/(2sqrt(3x-sin^2(4x)))

What is the first derivative of sqrt(3x-sin^2(4x)) ?

The first derivative of sqrt(3x-sin^2(4x)) is (3-4sin(8x))/(2sqrt(3x-sin^2(4x)))

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\frac{d}{d x} (3 x - sin^{2} (4 x))

\frac{3 - 4 sin ( 8 x )}{2 3 x - sin ^{2} ( 4 x )}

Solution steps

\frac{d}{d x} (3 x - sin^{2} (4 x))

Apply the chain rule:

\frac{1}{2 3 x - sin ^{2} ( 4 x )} \frac{d}{d x} (3 x - sin^{2} (4 x))

= \frac{1}{2 3 x - sin ^{2} ( 4 x )} \frac{d}{d x} (3 x - sin^{2} (4 x))

\frac{d}{d x} (3 x - sin^{2} (4 x)) = 3 - 4 sin (8 x)

= \frac{1}{2 3 x - sin ^{2} ( 4 x )} (3 - 4 sin (8 x))

Simplify

\frac{1}{2 3 x - sin ^{2} ( 4 x )} (3 - 4 sin (8 x)) : \frac{3 - 4 sin ( 8 x )}{2 3 x - sin ^{2} ( 4 x )}

= \frac{3 - 4 sin ( 8 x )}{2 3 x - sin ^{2} ( 4 x )}

x \to 0 lim (\frac{x}{e ^{7 x} - 1})

y^{^{'}} + 4 y = 32

x \to 3 lim (3)

\frac{e ^{- s}}{s ^{2} + s}

(sin (x^{3}))^{^{'}}

What is the derivative of sqrt(3x-sin^2(4x)) ?
The derivative of sqrt(3x-sin^2(4x)) is (3-4sin(8x))/(2sqrt(3x-sin^2(4x)))
What is the first derivative of sqrt(3x-sin^2(4x)) ?
The first derivative of sqrt(3x-sin^2(4x)) is (3-4sin(8x))/(2sqrt(3x-sin^2(4x)))