What is the derivative of 7sqrt(x)sin(x) ?

The derivative of 7sqrt(x)sin(x) is 7((sin(x))/(2sqrt(x))+sqrt(x)cos(x))

What is the first derivative of 7sqrt(x)sin(x) ?

The first derivative of 7sqrt(x)sin(x) is 7((sin(x))/(2sqrt(x))+sqrt(x)cos(x))

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derivative of

7 x sin (x)

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

Solution steps

\frac{d}{d x} (7 x sin (x))

Take the constant out:

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

= 7 \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)

= 7 (\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)

= 7 (\frac{1}{2 x} sin (x) + cos (x) x)

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

= 7 (\frac{sin ( x )}{2 x} + x cos (x))

\int \frac{8}{x ^{2} - 2 x + 2} d x

\frac{\partial}{\partial x} (x y - x - 3 y)

\int \frac{1 + sin ( x )}{1 + sin ( x ) - cos ( x )} d x

\int \frac{7}{x ^{3}} d x

y = x^{10} e^{x}

What is the derivative of 7sqrt(x)sin(x) ?
The derivative of 7sqrt(x)sin(x) is 7((sin(x))/(2sqrt(x))+sqrt(x)cos(x))
What is the first derivative of 7sqrt(x)sin(x) ?
The first derivative of 7sqrt(x)sin(x) is 7((sin(x))/(2sqrt(x))+sqrt(x)cos(x))