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

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

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

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

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derivative of

f (x) = x cos (x)

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = cos (x)

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} cos (x) + (- sin (x)) x

Simplify

\frac{1}{2 x} cos (x) + (- sin (x)) x : \frac{cos ( x )}{2 x} - x sin (x)

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

\int_{1}^{2} \frac{e ^{\frac{1}{x ^{5}}}}{x ^{6}} d x

x \to 2 - lim (x - a)

\int (9 - z^{2}) (6 - 2 z) d z

\int sin (2 x) e^{- s x} d x

\int_{4}^{\infty} e^{- 8 x} d x

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