What is the derivative of 2sin(8xcos(x)) ?

The derivative of 2sin(8xcos(x)) is 2(8cos(8x)cos(x)-sin(x)sin(8x))

What is the first derivative of 2sin(8xcos(x)) ?

The first derivative of 2sin(8xcos(x)) is 2(8cos(8x)cos(x)-sin(x)sin(8x))

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\frac{d}{d x} (2 sin (8 x) cos (x))

2 (8 cos (8 x) cos (x) - sin (x) sin (8 x))

Solution steps

\frac{d}{d x} (2 sin (8 x) cos (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (8 x), g = cos (x)

= 2 (\frac{d}{d x} (sin (8 x)) cos (x) + \frac{d}{d x} (cos (x)) sin (8 x))

\frac{d}{d x} (sin (8 x)) = cos (8 x) \cdot 8

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

= 2 (cos (8 x) \cdot 8 cos (x) + (- sin (x)) sin (8 x))

Simplify

= 2 (8 cos (8 x) cos (x) - sin (x) sin (8 x))

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

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

x \to π lim (\frac{( x ^{10} - π ^{10} )}{x - π})

\int x 5 - x d x

f (x) = ln (4^{x} + 8^{x})

What is the derivative of 2sin(8xcos(x)) ?
The derivative of 2sin(8xcos(x)) is 2(8cos(8x)cos(x)-sin(x)sin(8x))
What is the first derivative of 2sin(8xcos(x)) ?
The first derivative of 2sin(8xcos(x)) is 2(8cos(8x)cos(x)-sin(x)sin(8x))