Solve y=k/x - ScanMath

Simplify

y = \frac{k}{x}

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

\frac{\partial y}{\partial k} = \frac{\partial}{\partial k} (\frac{k}{x})

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 y}{\partial k} = \frac{\frac{\partial}{\partial k} ( k ) x - k \times \frac{\partial}{\partial k} ( x )}{x ^{2}}

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

\frac{\partial y}{\partial k} = \frac{1 \times x - k \times \frac{\partial}{\partial k} ( x )}{x ^{2}}

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

\frac{\partial y}{\partial k} = \frac{1 \times x - k \times 0}{x ^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial y}{\partial k} = \frac{x - k \times 0}{x ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial y}{\partial k} = \frac{x - 0}{x ^{2}}

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

\frac{\partial y}{\partial k} = \frac{x}{x ^{2}}

Solution

More Steps

\frac{\partial y}{\partial k} = \frac{1}{x}

Y=k/x