Solve \(x=\frac{a}{b}\)

Simplify

x = \frac{a}{b}

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

\frac{\partial x}{\partial a} = \frac{\partial}{\partial a} (\frac{a}{b})

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 x}{\partial a} = \frac{\frac{\partial}{\partial a} ( a ) b - a \times \frac{\partial}{\partial a} ( b )}{b ^{2}}

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

\frac{\partial x}{\partial a} = \frac{1 \times b - a \times \frac{\partial}{\partial a} ( b )}{b ^{2}}

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

\frac{\partial x}{\partial a} = \frac{1 \times b - a \times 0}{b ^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial x}{\partial a} = \frac{b - a \times 0}{b ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial x}{\partial a} = \frac{b - 0}{b ^{2}}

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

\frac{\partial x}{\partial a} = \frac{b}{b ^{2}}

Solution

More Steps

\frac{\partial x}{\partial a} = \frac{1}{b}

Function