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Popular >

derivative of sin(2xcos(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = sin (2 x), g = cos (x)

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

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

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

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

Simplify

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

Popular Examples

(\partial)/(\partial x)(tan(sqrt(x)))

\frac{\partial}{\partial x} (tan (x))

(d^4)/(dx^4)(3e^{x^2})

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

4y^{''}-4y^'+y=0

4 y^{^{''}} - 4 y^{^{'}} + y = 0

sum from n=1 to infinity of ln(1/(n^2))

n = 1 \sum \infty ln (\frac{1}{n ^{2}})

derivative of 2x(3x^2-7^3)

\frac{d}{d x} (2 x (3 x^{2} - 7)^{3})

Frequently Asked Questions (FAQ)

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