Solve beta=lambda/d

Simplify

β = \frac{λ}{d}

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

\frac{\partial β}{\partial λ} = \frac{\partial}{\partial λ} (\frac{λ}{d})

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 β}{\partial λ} = \frac{\frac{\partial}{\partial λ} ( λ ) d - λ \times \frac{\partial}{\partial λ} ( d )}{d ^{2}}

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

\frac{\partial β}{\partial λ} = \frac{1 \times d - λ \times \frac{\partial}{\partial λ} ( d )}{d ^{2}}

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

\frac{\partial β}{\partial λ} = \frac{1 \times d - λ \times 0}{d ^{2}}

Any expression multiplied by 1 remains the same

\frac{\partial β}{\partial λ} = \frac{d - λ \times 0}{d ^{2}}

Any expression multiplied by 0 equals 0

\frac{\partial β}{\partial λ} = \frac{d - 0}{d ^{2}}

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

\frac{\partial β}{\partial λ} = \frac{d}{d ^{2}}

Solution

More Steps

\frac{\partial β}{\partial λ} = \frac{1}{d}

Function