Solve c=f/lambda - ScanMath

Simplify

c = \frac{f}{λ}

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

\frac{\partial c}{\partial f} = \frac{\partial}{\partial f} (\frac{f}{λ})

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 c}{\partial f} = \frac{\frac{\partial}{\partial f} ( f ) λ - f \times \frac{\partial}{\partial f} ( λ )}{λ ^{2}}

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

\frac{\partial c}{\partial f} = \frac{1 \times λ - f \times \frac{\partial}{\partial f} ( λ )}{λ ^{2}}

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

\frac{\partial c}{\partial f} = \frac{1 \times λ - f \times 0}{λ ^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial c}{\partial f} = \frac{λ - f \times 0}{λ ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial c}{\partial f} = \frac{λ - 0}{λ ^{2}}

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

\frac{\partial c}{\partial f} = \frac{λ}{λ ^{2}}

Solution

More Steps

\frac{\partial c}{\partial f} = \frac{1}{λ}

Function