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

The derivative of f(x)=sin(x)cos(x) is cos(2x)

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

The first derivative of f(x)=sin(x)cos(x) is cos(2x)

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derivative of

f (x) = sin (x) cos (x)

cos (2 x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

Simplify

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

= cos (2 x)

f (x) = 4^{x}

x - y = - 2

f (x) = x^{2} + 3

x^{2} e^{- x}

f (m) = \frac{1}{lo g _{3} ( m )}

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