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Popular >

derivative of 4x*sin(x)

Solution

\frac{d}{d x} (4 x \cdot 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-sin(3x)

\int - sin (3 x) d x

sum from n=0 to infinity of (t^n)/(n!)

n = 0 \sum \infty \frac{t ^{n}}{n !}

derivative of (sqrt(x+1)+sqrt(x-1)^4)

\frac{d}{d x} ((x + 1 + x - 1)^{4})

(\partial)/(\partial x)(2x^2w^3(z-1))

\frac{\partial}{\partial x} (2 x^{2} w^{3} (z - 1))

derivative of (6-x^{-1})

\frac{d}{d x} ((6 - x)^{- 1})

Frequently Asked Questions (FAQ)

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