What is (\partial)/(\partial x)(x^2tan(xy)) ?

The answer to (\partial)/(\partial x)(x^2tan(xy)) is 2xtan(xy)+sec^2(xy)yx^2

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(\partial)/(\partial x)(x^2tan(xy))

\frac{\partial}{\partial x} (x^{2} tan (x y))

2 x tan (x y) + sec^{2} (x y) y x^{2}

Solution steps

\frac{\partial}{\partial x} (x^{2} tan (x y))

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

\frac{\partial}{\partial x} (tan (x y)) = sec^{2} (x y) y

= 2 x tan (x y) + sec^{2} (x y) y x^{2}

What is (\partial)/(\partial x)(x^2tan(xy)) ?
The answer to (\partial)/(\partial x)(x^2tan(xy)) is 2xtan(xy)+sec^2(xy)yx^2