What is the derivative of 6sin(xcos(x)) ?

The derivative of 6sin(xcos(x)) is 6cos(2x)

What is the first derivative of 6sin(xcos(x)) ?

The first derivative of 6sin(xcos(x)) is 6cos(2x)

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\frac{d}{d x} (6 sin (x) cos (x))

6 cos (2 x)

Solution steps

\frac{d}{d x} (6 sin (x) cos (x))

Simplify

6 sin (x) cos (x) : 3 sin (2 x)

= \frac{d}{d x} (3 sin (2 x))

Take the constant out:

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

= 3 \frac{d}{d x} (sin (2 x))

Apply the chain rule:

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

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

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

= 3 cos (2 x) \cdot 2

Simplify

= 6 cos (2 x)

\int_{0}^{2} \frac{y}{9 - y ^{2}} d y

\int \frac{( 5 x + 3 )}{x ^{3} - 2 x ^{2} - 3 x} d x

y^{^{'}} = x^{2} \cdot y

x \to 2 + lim (5)

\int \frac{8 x ^{2} - 13 x + 2}{x ^{3} - 3 x ^{2} + 2 x} d x

What is the derivative of 6sin(xcos(x)) ?
The derivative of 6sin(xcos(x)) is 6cos(2x)
What is the first derivative of 6sin(xcos(x)) ?
The first derivative of 6sin(xcos(x)) is 6cos(2x)