partial derivative of cos(xln(y)) with respect to x

⚠ cos(xln(y)) is read as cos(x*ln(y)): use * for multiplication, use ^ for a power

Differentiate with respect to x while holding y constant

Let's perform the differentiation:

\frac{\partial}{\partial x} (\cos (x \cdot \ln (y)))

We differentiate using:

\frac{\partial}{\partial x} (\cos (f)) = - \frac{\partial}{\partial x} (f) \cdot \sin (f)

(where f =

x \cdot \ln (y)

)

ⓘ The derivative of cos(x) is -sin(x):

\frac{\partial}{\partial x} (\cos (x \cdot \ln (y)))

- \frac{\partial}{\partial x} (x \cdot \ln (y)) \cdot \sin (x \cdot \ln (y))

- \frac{\partial}{\partial x} (x \cdot \ln (y)) \cdot \sin (x \cdot \ln (y))

ⓘ For differentiation with respect to

x

\ln (y)

is treated as constant. A constant factor stays in front of the derivative, (k*u)' = k*u':

\frac{\partial}{\partial x} (x \cdot \ln (y))

\ln (y) \cdot \frac{\partial}{\partial x} (x)

\ln (y) \cdot 1

\ln (y)

▶Derivative:

- \ln (y) \cdot \sin (x \cdot \ln (y))