Solve p=2sigma/r - ScanMath

Evaluate

p = 2 \times \frac{σ}{r}

Multiply the terms

p = \frac{2 σ}{r}

Find the first partial derivative by treating the variable r as a constant and differentiating with respect to σ

\frac{\partial p}{\partial σ} = \frac{\partial}{\partial σ} (\frac{2 σ}{r})

Use differentiation rule \frac{\partial}{\partial x} (\frac{f ( x )}{g ( x )}) = \frac{\frac{\partial}{\partial x} ( f ( x )) \times g ( x ) - f ( x ) \times \frac{\partial}{\partial x} ( g ( x ) )}{( g ( x ) ) ^{2}}

\frac{\partial p}{\partial σ} = \frac{\frac{\partial}{\partial σ} ( 2 σ ) r - 2 σ \times \frac{\partial}{\partial σ} ( r )}{r ^{2}}

Evaluate

More Steps

\frac{\partial p}{\partial σ} = \frac{2 r - 2 σ \times \frac{\partial}{\partial σ} ( r )}{r ^{2}}

Use \frac{\partial}{\partial x} (c) = 0 to find derivative

\frac{\partial p}{\partial σ} = \frac{2 r - 2 σ \times 0}{r ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial p}{\partial σ} = \frac{2 r - 0}{r ^{2}}

Removing 0 doesn't change the value,so remove it from the expression

\frac{\partial p}{\partial σ} = \frac{2 r}{r ^{2}}

Solution

More Steps

\frac{\partial p}{\partial σ} = \frac{2}{r}

P=2sigma/r