What is the derivative of (75/(sqrt(12+x^2+y^2))) ?

The derivative of (75/(sqrt(12+x^2+y^2))) is -(75(x+y\frac{dy)/(dx))}{(12+x^2+y^2)^{3/2}}

What is the first derivative of (75/(sqrt(12+x^2+y^2))) ?

The first derivative of (75/(sqrt(12+x^2+y^2))) is -(75(x+y\frac{dy)/(dx))}{(12+x^2+y^2)^{3/2}}

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\frac{d}{d x} (\frac{75}{12 + x ^{2} + y ^{2}})

- \frac{75 ( x + y \frac{d y}{d x} )}{( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{75}{12 + x ^{2} + y ^{2}})

Take the constant out:

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

= 75 \frac{d}{d x} (\frac{1}{12 + x ^{2} + y ^{2}})

Apply exponent rule:

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

= 75 \frac{d}{d x} ((12 + x^{2} + y^{2})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (12 + x^{2} + y^{2})

= - \frac{1}{2 ( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (12 + x^{2} + y^{2})

\frac{d}{d x} (12 + x^{2} + y^{2}) = 2 x + 2 y \frac{d y}{d x}

= 75 (- \frac{1}{2 ( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}} (2 x + 2 y \frac{d y}{d x}))

Simplify

75 (- \frac{1}{2 ( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}} (2 x + 2 y \frac{d y}{d x})) : - \frac{75 ( x + y \frac{d y}{d x} )}{( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

= - \frac{75 ( x + y \frac{d y}{d x} )}{( 12 + x ^{2} + y ^{2} ) ^{\frac{3}{2}}}

\int \frac{- 2 x}{x ^{2} + 4} d x

x \to 3 lim (x 18 - x^{2})

\frac{d}{d x} ((x^{2} + 1) (x^{3} + 1))

y = 2 e^{x} cos (x)

\frac{( \frac{1}{2} )}{s}

What is the derivative of (75/(sqrt(12+x^2+y^2))) ?
The derivative of (75/(sqrt(12+x^2+y^2))) is -(75(x+y\frac{dy)/(dx))}{(12+x^2+y^2)^{3/2}}
What is the first derivative of (75/(sqrt(12+x^2+y^2))) ?
The first derivative of (75/(sqrt(12+x^2+y^2))) is -(75(x+y\frac{dy)/(dx))}{(12+x^2+y^2)^{3/2}}