What is (\partial)/(\partial x)(tan(4xy^5)) ?

The answer to (\partial)/(\partial x)(tan(4xy^5)) is sec^2(4xy^5)*4y^5

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(\partial)/(\partial x)(tan(4xy^5))

\frac{\partial}{\partial x} (tan (4 x y^{5}))

sec^{2} (4 x y^{5}) \cdot 4 y^{5}

Solution steps

\frac{\partial}{\partial x} (tan (4 x y^{5}))

Treat

y

as a constant

Apply the chain rule:

sec^{2} (4 x y^{5}) \frac{\partial}{\partial x} (4 x y^{5})

= sec^{2} (4 x y^{5}) \frac{\partial}{\partial x} (4 x y^{5})

\frac{\partial}{\partial x} (4 x y^{5}) = 4 y^{5}

= sec^{2} (4 x y^{5}) \cdot 4 y^{5}

\frac{d}{d x} (\frac{2 x ^{2} + x - 1}{x ^{2} - 1})

x^{2} - 2 x + 3, x = - 2, x = 1

\frac{d}{d x} ((2 x^{2} - 6)^{- 10})

y^{^{''}} - 8 y^{^{'}} + 16 y = t - 2 e^{4 t}

\int (x^{3} - 1)^{2} d x

What is (\partial)/(\partial x)(tan(4xy^5)) ?
The answer to (\partial)/(\partial x)(tan(4xy^5)) is sec^2(4xy^5)*4y^5