What is the derivative of f(x)=8sqrt(x)sin(x) ?

The derivative of f(x)=8sqrt(x)sin(x) is 8((sin(x))/(2sqrt(x))+sqrt(x)cos(x))

What is the first derivative of f(x)=8sqrt(x)sin(x) ?

The first derivative of f(x)=8sqrt(x)sin(x) is 8((sin(x))/(2sqrt(x))+sqrt(x)cos(x))

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derivative of

f (x) = 8 x sin (x)

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

Solution steps

\frac{d}{d x} (8 x sin (x))

Take the constant out:

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

= 8 \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)

= 8 (\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)

= 8 (\frac{1}{2 x} sin (x) + cos (x) x)

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

= 8 (\frac{sin ( x )}{2 x} + x cos (x))

What is the derivative of f(x)=8sqrt(x)sin(x) ?
The derivative of f(x)=8sqrt(x)sin(x) is 8((sin(x))/(2sqrt(x))+sqrt(x)cos(x))
What is the first derivative of f(x)=8sqrt(x)sin(x) ?
The first derivative of f(x)=8sqrt(x)sin(x) is 8((sin(x))/(2sqrt(x))+sqrt(x)cos(x))