What is (\partial)/(\partial x)(x^2cos(xln(y))) ?

The answer to (\partial)/(\partial x)(x^2cos(xln(y))) is 2xcos(xln(y))-x^2sin(xln(y))ln(y)

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(\partial)/(\partial x)(x^2cos(xln(y)))

\frac{\partial}{\partial x} (x^{2} cos (x ln (y)))

2 x cos (x ln (y)) - x^{2} sin (x ln (y)) ln (y)

Solution steps

\frac{\partial}{\partial x} (x^{2} cos (x ln (y)))

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = cos (x ln (y))

= \frac{\partial}{\partial x} (x^{2}) cos (x ln (y)) + \frac{\partial}{\partial x} (cos (x ln (y))) x^{2}

\frac{\partial}{\partial x} (x^{2}) = 2 x

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

= 2 x cos (x ln (y)) + (- sin (x ln (y)) ln (y)) x^{2}

Simplify

= 2 x cos (x ln (y)) - x^{2} sin (x ln (y)) ln (y)

\int 36 e^{- 6 x} sin (6 x) d x

\int (x - 2) (x^{2} - 4 x + 9) d x

\int 2 x^{2} e^{2 x} d x

\frac{\partial}{\partial s} (s t)

x^{4} - 2 x^{3} + 5

What is (\partial)/(\partial x)(x^2cos(xln(y))) ?
The answer to (\partial)/(\partial x)(x^2cos(xln(y))) is 2xcos(xln(y))-x^2sin(xln(y))ln(y)