What is the derivative of f(x)=5sqrt(x)sin(x) ?

The derivative of f(x)=5sqrt(x)sin(x) is 5((sin(x))/(2sqrt(x))+sqrt(x)cos(x))

What is the first derivative of f(x)=5sqrt(x)sin(x) ?

The first derivative of f(x)=5sqrt(x)sin(x) is 5((sin(x))/(2sqrt(x))+sqrt(x)cos(x))

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derivative of

f (x) = 5 x sin (x)

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = sin (x)

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

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

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

= 5 (\frac{1}{2 x} sin (x) + cos (x) x)

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

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

\int_{0}^{π} cos (2 x) d x

\int \frac{x}{x ^{2} - 3} d x

\frac{1}{x ( x ^{2} + 2 x + x )}

f (x) = 3 ln (x)

\frac{d}{d x} (\frac{1}{6 x + 5})

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