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

The derivative of sin(4x+sin^2(4x)) is cos(4x)*4+4sin(8x)

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

The first derivative of sin(4x+sin^2(4x)) is cos(4x)*4+4sin(8x)

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

cos (4 x) \cdot 4 + 4 sin (8 x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

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

= cos (4 x) \cdot 4 + 4 sin (8 x)

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

\frac{d ^{2} x}{d t} + 2 \frac{d x}{d t} + x = 1

\int 5 + x^{2} d x

y = 8 x, y = 4 x^{2}

\frac{\partial}{\partial y} (2 e^{x} ln (y))

What is the derivative of sin(4x+sin^2(4x)) ?
The derivative of sin(4x+sin^2(4x)) is cos(4x)*4+4sin(8x)
What is the first derivative of sin(4x+sin^2(4x)) ?
The first derivative of sin(4x+sin^2(4x)) is cos(4x)*4+4sin(8x)