What is the derivative of 5xsin(xcos(x)) ?

The derivative of 5xsin(xcos(x)) is 5(sin(x)cos(x)+xcos(2x))

What is the first derivative of 5xsin(xcos(x)) ?

The first derivative of 5xsin(xcos(x)) is 5(sin(x)cos(x)+xcos(2x))

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\frac{d}{d x} (5 x sin (x) cos (x))

5 (sin (x) cos (x) + x cos (2 x))

Solution steps

\frac{d}{d x} (5 x sin (x) cos (x))

Take the constant out:

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

= 5 \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)

= 5 (\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)

= 5 (1 \cdot sin (x) cos (x) + cos (2 x) x)

Simplify

= 5 (sin (x) cos (x) + x cos (2 x))

\int (3 - x) d x

\int_{0}^{l n (π)} 2 x e^{x^{2}} cos (e^{x^{2}}) d x

x \to - 6 - lim (x^{2} + \frac{2}{x + 6})

\frac{\partial}{\partial x} (1 + 2 x)

9 - x^{2}, x

What is the derivative of 5xsin(xcos(x)) ?
The derivative of 5xsin(xcos(x)) is 5(sin(x)cos(x)+xcos(2x))
What is the first derivative of 5xsin(xcos(x)) ?
The first derivative of 5xsin(xcos(x)) is 5(sin(x)cos(x)+xcos(2x))