What is the derivative of f(x)=4xsin(x)cos(x) ?

The derivative of f(x)=4xsin(x)cos(x) is 4(sin(x)cos(x)+xcos(2x))

What is the first derivative of f(x)=4xsin(x)cos(x) ?

The first derivative of f(x)=4xsin(x)cos(x) is 4(sin(x)cos(x)+xcos(2x))

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derivative of

f (x) = 4 x sin (x) cos (x)

4 (sin (x) cos (x) + x cos (2 x))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 4 (1 \cdot sin (x) cos (x) + cos (2 x) x)

Simplify

= 4 (sin (x) cos (x) + x cos (2 x))

(- 3, - 10), (4, 5)

y = 5 x^{4} f (x)

20 y^{^{''}} - y^{^{'}} + 7 y = 0

\frac{d}{d x} (\frac{n}{x})

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

What is the derivative of f(x)=4xsin(x)cos(x) ?
The derivative of f(x)=4xsin(x)cos(x) is 4(sin(x)cos(x)+xcos(2x))
What is the first derivative of f(x)=4xsin(x)cos(x) ?
The first derivative of f(x)=4xsin(x)cos(x) is 4(sin(x)cos(x)+xcos(2x))