What is the derivative of (sqrt(25-x^2)/(8x)) ?

The derivative of (sqrt(25-x^2)/(8x)) is -(25)/(8x^2sqrt(25-x^2))

What is the first derivative of (sqrt(25-x^2)/(8x)) ?

The first derivative of (sqrt(25-x^2)/(8x)) is -(25)/(8x^2sqrt(25-x^2))

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\frac{d}{d x} (\frac{25 - x ^{2}}{8 x})

- \frac{25}{8 x ^{2} 25 - x ^{2}}

Solution steps

\frac{d}{d x} (\frac{25 - x ^{2}}{8 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{8} \frac{d}{d x} (\frac{25 - x ^{2}}{x})

Apply the Quotient Rule:

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

= \frac{1}{8} \cdot \frac{\frac{d}{d x} ( 25 - x ^{2} ) x - \frac{d x}{d x} 25 - x ^{2}}{x ^{2}}

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

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

= \frac{1}{8} \cdot \frac{( - \frac{x}{25 - x ^{2}} ) x - 1 \cdot 25 - x ^{2}}{x ^{2}}

Simplify

\frac{1}{8} \cdot \frac{( - \frac{x}{25 - x ^{2}} ) x - 1 \cdot 25 - x ^{2}}{x ^{2}} : - \frac{25}{8 x ^{2} 25 - x ^{2}}

= - \frac{25}{8 x ^{2} 25 - x ^{2}}

\int \frac{30}{1 - cos ( 6 x )} d x

\int \frac{18}{1 - cos ( 3 x )} d x

- 7 x^{3} e^{x} - 21 x^{2} e^{x}

x \to 2 + lim ((x - 2)^{2})

3 x^{2} + 6 x + 4

What is the derivative of (sqrt(25-x^2)/(8x)) ?
The derivative of (sqrt(25-x^2)/(8x)) is -(25)/(8x^2sqrt(25-x^2))
What is the first derivative of (sqrt(25-x^2)/(8x)) ?
The first derivative of (sqrt(25-x^2)/(8x)) is -(25)/(8x^2sqrt(25-x^2))