What is the derivative of 1/(sqrt(y-5x^2)) ?

The derivative of 1/(sqrt(y-5x^2)) is -(\frac{dy)/(dx)-10x}{2(y-5x^2)^{3/2}}

What is the first derivative of 1/(sqrt(y-5x^2)) ?

The first derivative of 1/(sqrt(y-5x^2)) is -(\frac{dy)/(dx)-10x}{2(y-5x^2)^{3/2}}

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\frac{d}{d x} (\frac{1}{y - 5 x ^{2}})

- \frac{\frac{d y}{d x} - 10 x}{2 ( y - 5 x ^{2} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{1}{y - 5 x ^{2}})

Apply exponent rule:

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

= \frac{d}{d x} ((y - 5 x^{2})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( y - 5 x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (y - 5 x^{2})

= - \frac{1}{2 ( y - 5 x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (y - 5 x^{2})

\frac{d}{d x} (y - 5 x^{2}) = \frac{d y}{d x} - 10 x

= - \frac{1}{2 ( y - 5 x ^{2} ) ^{\frac{3}{2}}} (\frac{d y}{d x} - 10 x)

Simplify

- \frac{1}{2 ( y - 5 x ^{2} ) ^{\frac{3}{2}}} (\frac{d y}{d x} - 10 x) : - \frac{\frac{d y}{d x} - 10 x}{2 ( y - 5 x ^{2} ) ^{\frac{3}{2}}}

= - \frac{\frac{d y}{d x} - 10 x}{2 ( y - 5 x ^{2} ) ^{\frac{3}{2}}}

y^{^{'}} - y = 2 t

x^{2} y^{^{'}} + 2 x y = 25 cos^{2} (x)

\frac{- 8 x}{x ^{2} + 1}

\frac{5}{s ( s ^{2} + 4 s + 5 )}

\int \frac{6 x + 7}{( x + 2 ) ^{2}} d x

What is the derivative of 1/(sqrt(y-5x^2)) ?
The derivative of 1/(sqrt(y-5x^2)) is -(\frac{dy)/(dx)-10x}{2(y-5x^2)^{3/2}}
What is the first derivative of 1/(sqrt(y-5x^2)) ?
The first derivative of 1/(sqrt(y-5x^2)) is -(\frac{dy)/(dx)-10x}{2(y-5x^2)^{3/2}}