What is the derivative of (sin(x)/(x^5)) ?

The derivative of (sin(x)/(x^5)) is (xcos(x)-5sin(x))/(x^6)

What is the first derivative of (sin(x)/(x^5)) ?

The first derivative of (sin(x)/(x^5)) is (xcos(x)-5sin(x))/(x^6)

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

\frac{x cos ( x ) - 5 sin ( x )}{x ^{6}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( sin ( x ) ) x ^{5} - \frac{d}{d x} ( x ^{5} ) sin ( x )}{( x ^{5} ) ^{2}}

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

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

= \frac{cos ( x ) x ^{5} - 5 x ^{4} sin ( x )}{( x ^{5} ) ^{2}}

Simplify

\frac{cos ( x ) x ^{5} - 5 x ^{4} sin ( x )}{( x ^{5} ) ^{2}} : \frac{x cos ( x ) - 5 sin ( x )}{x ^{6}}

= \frac{x cos ( x ) - 5 sin ( x )}{x ^{6}}

\frac{d}{d x} (x^{4} - 2 x^{2} + 3)

x^{3} - 2 x + 1

y = (x^{3} - 9 x)^{10}, (3, 0)

y = 3 x^{3} - 3 x, (- 4, 0)

\int_{0}^{3} (5 - \frac{5}{3} x)^{2} d x

What is the derivative of (sin(x)/(x^5)) ?
The derivative of (sin(x)/(x^5)) is (xcos(x)-5sin(x))/(x^6)
What is the first derivative of (sin(x)/(x^5)) ?
The first derivative of (sin(x)/(x^5)) is (xcos(x)-5sin(x))/(x^6)