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Popular >

derivative of 4sqrt(x)sin(x)

Solution

derivative of

4 x sin (x)

Solution

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

Solution steps

\frac{d}{d x} (4 x sin (x))

Take the constant out:

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

= 4 \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)

= 4 (\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)

= 4 (\frac{1}{2 x} sin (x) + cos (x) x)

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

= 4 (\frac{sin ( x )}{2 x} + x cos (x))

Popular Examples

- 4 y^{^{'}} + 12 x^{2} = 0

(\partial)/(\partial x)(3y^2cos(5x))

\frac{\partial}{\partial x} (3 y^{2} cos (5 x))

(\partial)/(\partial x)(2xye^{xy^2}-3y^2)

\frac{\partial}{\partial x} (2 x y e^{x y^{2}} - 3 y^{2})

integral of 1/((ln(x))^2)

\int \frac{1}{( ln ( x ) ) ^{2}} d x

(\partial)/(\partial y)(2arctan(y/x))

\frac{\partial}{\partial y} (2 arctan (\frac{y}{x}))

Frequently Asked Questions (FAQ)

What is the derivative of 4sqrt(x)sin(x) ?
The derivative of 4sqrt(x)sin(x) is 4((sin(x))/(2sqrt(x))+sqrt(x)cos(x))
What is the first derivative of 4sqrt(x)sin(x) ?
The first derivative of 4sqrt(x)sin(x) is 4((sin(x))/(2sqrt(x))+sqrt(x)cos(x))