en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (sin(4x)/x)

Solution

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

Solution

\frac{4 x cos ( 4 x ) - sin ( 4 x )}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

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

= \frac{cos ( 4 x ) \cdot 4 x - 1 \cdot sin ( 4 x )}{x ^{2}}

Simplify

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

Popular Examples

integral from 1 to 2 of 12x^22^{x^3}

\int_{1}^{2} 12 x^{2} 2^{x^{3}} d x

y^{''}+2sqrt(6)y^'+6y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 26 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 0

f(x)=(x+5)cos(x)

f (x) = (x + 5) cos (x)

inverse oflaplace (2s+9)/((s+4)(s+6))inverse laplace

\frac{2 s + 9}{( s + 4 ) ( s + 6 )}

integral from 0 to 2 of x^3e^{x^2}

\int_{0}^{2} x^{3} e^{x^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (sin(4x)/x) ?
The derivative of (sin(4x)/x) is (4xcos(4x)-sin(4x))/(x^2)
What is the first derivative of (sin(4x)/x) ?
The first derivative of (sin(4x)/x) is (4xcos(4x)-sin(4x))/(x^2)