What is the derivative of 1/(sqrt(-25x^2+2y^2-50)) ?

The derivative of 1/(sqrt(-25x^2+2y^2-50)) is -(-25x+2y\frac{dy)/(dx)}{(-25x^2+2y^2-50)^{3/2}}

What is the first derivative of 1/(sqrt(-25x^2+2y^2-50)) ?

The first derivative of 1/(sqrt(-25x^2+2y^2-50)) is -(-25x+2y\frac{dy)/(dx)}{(-25x^2+2y^2-50)^{3/2}}

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\frac{d}{d x} (\frac{1}{- 25 x ^{2} + 2 y ^{2} - 50})

- \frac{- 25 x + 2 y \frac{d y}{d x}}{( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{- 25 x ^{2} + 2 y ^{2} - 50})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((- 25 x^{2} + 2 y^{2} - 50)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}} \frac{d}{d x} (- 25 x^{2} + 2 y^{2} - 50)

= - \frac{1}{2 ( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}} \frac{d}{d x} (- 25 x^{2} + 2 y^{2} - 50)

\frac{d}{d x} (- 25 x^{2} + 2 y^{2} - 50) = - 50 x + 4 y \frac{d y}{d x}

= - \frac{1}{2 ( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}} (- 50 x + 4 y \frac{d y}{d x})

Simplify

- \frac{1}{2 ( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}} (- 50 x + 4 y \frac{d y}{d x}) : - \frac{- 25 x + 2 y \frac{d y}{d x}}{( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}}

= - \frac{- 25 x + 2 y \frac{d y}{d x}}{( - 25 x ^{2} + 2 y ^{2} - 50 ) ^{\frac{3}{2}}}

x \to 4 lim (x + x)

y = ln (x x^{2} - 2)

(6, - 1), (8, 3)

\frac{d}{d x} (\frac{ln ( x )}{x ^{\frac{6}{5}}})

d ln (x) + a x^{n} + b e^{x}

What is the derivative of 1/(sqrt(-25x^2+2y^2-50)) ?
The derivative of 1/(sqrt(-25x^2+2y^2-50)) is -(-25x+2y\frac{dy)/(dx)}{(-25x^2+2y^2-50)^{3/2}}
What is the first derivative of 1/(sqrt(-25x^2+2y^2-50)) ?
The first derivative of 1/(sqrt(-25x^2+2y^2-50)) is -(-25x+2y\frac{dy)/(dx)}{(-25x^2+2y^2-50)^{3/2}}