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

The answer to (\partial)/(\partial x)(y^2tan(xy)) is y^3sec^2(yx)

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

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

y^{3} sec^{2} (y x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (x y) = y

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

Simplify

y^{2} sec^{2} (x y) y : y^{3} sec^{2} (y x)

= y^{3} sec^{2} (y x)

5 e^{2 x}

\frac{d}{d x} (6 x^{- 1})

5 (x^{6} - 8)^{5}

f (x) = 4 x + 3 x^{2}, at x = 2

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

What is (\partial)/(\partial x)(y^2tan(xy)) ?
The answer to (\partial)/(\partial x)(y^2tan(xy)) is y^3sec^2(yx)