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Popular >

derivative of 3cos(xsin(x))

Solution

\frac{d}{d x} (3 cos (x) sin (x))

Solution

3 cos (2 x)

Solution steps

\frac{d}{d x} (3 cos (x) sin (x))

Take the constant out:

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

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

Apply the Product Rule:

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

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

= 3 (\frac{d}{d x} (cos (x)) sin (x) + \frac{d}{d x} (sin (x)) cos (x))

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

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

= 3 ((- sin (x)) sin (x) + cos (x) cos (x))

Simplify

3 ((- sin (x)) sin (x) + cos (x) cos (x)) : 3 cos (2 x)

= 3 cos (2 x)

Popular Examples

integral of ((x-2))/x

\int \frac{( x - 2 )}{x} d x

tangent of f(x)=4x^3-4x,(-1,0)tangent of

f (x) = 4 x^{3} - 4 x, (- 1, 0)

tangent of f(x)=2e^{2x^2+3x},\at x=0 tangent of

f (x) = 2 e^{2 x^{2} + 3 x}, at x = 0

integral of 1/((x+2)(x-2))

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

(\partial)/(\partial x)(sin(5pix+4y))

\frac{\partial}{\partial x} (sin (5 π x + 4 y))

Frequently Asked Questions (FAQ)

What is the derivative of 3cos(xsin(x)) ?
The derivative of 3cos(xsin(x)) is 3cos(2x)
What is the first derivative of 3cos(xsin(x)) ?
The first derivative of 3cos(xsin(x)) is 3cos(2x)