What is the derivative of f(x)=cos(2*x)*sin(5*x) ?

The derivative of f(x)=cos(2*x)*sin(5*x) is -2sin(2x)sin(5x)+5cos(5x)cos(2x)

What is the first derivative of f(x)=cos(2*x)*sin(5*x) ?

The first derivative of f(x)=cos(2*x)*sin(5*x) is -2sin(2x)sin(5x)+5cos(5x)cos(2x)

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derivative of

f (x) = cos (2 \cdot x) \cdot sin (5 \cdot x)

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

Solution steps

\frac{d}{d x} (cos (2 x) sin (5 x))

Apply the Product Rule:

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

f = cos (2 x), g = sin (5 x)

= \frac{d}{d x} (cos (2 x)) sin (5 x) + \frac{d}{d x} (sin (5 x)) cos (2 x)

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

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

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

Simplify

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

\frac{d}{d x} (\frac{x ^{4} - 1}{x ^{4} + 1})

\frac{d}{d x} ((x^{4} - 3 x^{2} + 5)^{3})

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

f (x) = x^{2} - 8 x - 8

\frac{\partial}{\partial x} (x^{6} y^{8} - x^{5} y^{7})

What is the derivative of f(x)=cos(2*x)*sin(5*x) ?
The derivative of f(x)=cos(2*x)*sin(5*x) is -2sin(2x)sin(5x)+5cos(5x)cos(2x)
What is the first derivative of f(x)=cos(2*x)*sin(5*x) ?
The first derivative of f(x)=cos(2*x)*sin(5*x) is -2sin(2x)sin(5x)+5cos(5x)cos(2x)