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Popular >

derivative of (sin(3x)/x)

Solution

\frac{d}{d x} (\frac{sin ( 3 x )}{x})

Solution

\frac{3 x cos ( 3 x ) - sin ( 3 x )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{sin ( 3 x )}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( sin ( 3 x ) ) x - \frac{d x}{d x} sin ( 3 x )}{x ^{2}}

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

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

= \frac{cos ( 3 x ) \cdot 3 x - 1 \cdot sin ( 3 x )}{x ^{2}}

Simplify

= \frac{3 x cos ( 3 x ) - sin ( 3 x )}{x ^{2}}

Popular Examples

6y^{''}+8y^'+y=0,y(-2)=-3,y^'(-2)=-4

6 y^{^{''}} + 8 y^{^{'}} + y = 0, y (- 2) = - 3, y^{^{'}} (- 2) = - 4

integral of (7x+1)/(6x^2+x-1)

\int \frac{7 x + 1}{6 x ^{2} + x - 1} d x

limit as x approaches 4 of-(15)/(x-4)

x \to 4 lim (- \frac{15}{x - 4})

(\partial)/(\partial x)(sin(pix))

\frac{\partial}{\partial x} (sin (π x))

derivative of 4x^5

\frac{d}{d x} (4 x^{5})

Frequently Asked Questions (FAQ)

What is the derivative of (sin(3x)/x) ?
The derivative of (sin(3x)/x) is (3xcos(3x)-sin(3x))/(x^2)
What is the first derivative of (sin(3x)/x) ?
The first derivative of (sin(3x)/x) is (3xcos(3x)-sin(3x))/(x^2)