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Popular >

derivative of 4xsin(x)

Solution

derivative of

4 x sin (x)

Solution

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

\frac{d x}{d x} = 1

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

= 4 (1 \cdot sin (x) + cos (x) x)

Simplify

= 4 (sin (x) + x cos (x))

Popular Examples

integral of 1/(sec(2x))

\int \frac{1}{sec ( 2 x )} d x

limit as x approaches 11+of sqrt(x-11)

x \to 11 + lim (x - 11)

(dy)/(dx)=sin(2x)-1/2 sin(4x)

\frac{d y}{d x} = sin (2 x) - \frac{1}{2} sin (4 x)

tangent of f(x)=x(1-2x)^3,(1,-1)tangent of

f (x) = x (1 - 2 x)^{3}, (1, - 1)

(\partial)/(\partial w)(1/(2sqrt(v-w)))

\frac{\partial}{\partial w} (\frac{1}{2 v - w})

Frequently Asked Questions (FAQ)

What is the derivative of 4xsin(x) ?
The derivative of 4xsin(x) is 4(sin(x)+xcos(x))
What is the first derivative of 4xsin(x) ?
The first derivative of 4xsin(x) is 4(sin(x)+xcos(x))