What is the derivative of y=(cos(x))/(x^7) ?

The derivative of y=(cos(x))/(x^7) is -(xsin(x)+7cos(x))/(x^8)

What is the first derivative of y=(cos(x))/(x^7) ?

The first derivative of y=(cos(x))/(x^7) is -(xsin(x)+7cos(x))/(x^8)

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derivative of

y = \frac{cos ( x )}{x ^{7}}

- \frac{x sin ( x ) + 7 cos ( x )}{x ^{8}}

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{x ^{7}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( cos ( x ) ) x ^{7} - \frac{d}{d x} ( x ^{7} ) cos ( x )}{( x ^{7} ) ^{2}}

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{( - sin ( x ) ) x ^{7} - 7 x ^{6} cos ( x )}{( x ^{7} ) ^{2}}

Simplify

\frac{( - sin ( x ) ) x ^{7} - 7 x ^{6} cos ( x )}{( x ^{7} ) ^{2}} : - \frac{x sin ( x ) + 7 cos ( x )}{x ^{8}}

= - \frac{x sin ( x ) + 7 cos ( x )}{x ^{8}}

x \to 0 lim (\frac{sin ( 2 x )}{x})

y^{^{'}} = - y^{3}, y (0) = 2

\frac{\partial}{\partial x} (7 x cos (x y))

7 y^{^{''}} + y = 0

\int e^{4 x} \frac{1}{5} d x

What is the derivative of y=(cos(x))/(x^7) ?
The derivative of y=(cos(x))/(x^7) is -(xsin(x)+7cos(x))/(x^8)
What is the first derivative of y=(cos(x))/(x^7) ?
The first derivative of y=(cos(x))/(x^7) is -(xsin(x)+7cos(x))/(x^8)