Solve x=r sinf - ScanMath

Simplify

x = r sin (f)

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

\frac{\partial x}{\partial r} = \frac{\partial}{\partial r} (r sin (f))

Use differentiation rule \frac{\partial}{\partial x} (f (x) \times g (x)) = \frac{\partial}{\partial x} (f (x)) \times g (x) + f (x) \times \frac{\partial}{\partial x} (g (x))

\frac{\partial x}{\partial r} = \frac{\partial}{\partial r} (r) sin (f) + r \times \frac{\partial}{\partial r} (sin (f))

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

\frac{\partial x}{\partial r} = 1 \times sin (f) + r \times \frac{\partial}{\partial r} (sin (f))

Evaluate

\frac{\partial x}{\partial r} = sin (f) + r \times \frac{\partial}{\partial r} (sin (f))

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

\frac{\partial x}{\partial r} = sin (f) + r \times 0

Evaluate

\frac{\partial x}{\partial r} = sin (f) + 0

Solution

\frac{\partial x}{\partial r} = sin (f)

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