What is (\partial)/(\partial x)(sin(7x^5y-7xy^4)) ?

The answer to (\partial)/(\partial x)(sin(7x^5y-7xy^4)) is cos(7x^5y-7xy^4)(35yx^4-7y^4)

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(\partial)/(\partial x)(sin(7x^5y-7xy^4))

\frac{\partial}{\partial x} (sin (7 x^{5} y - 7 x y^{4}))

cos (7 x^{5} y - 7 x y^{4}) (35 y x^{4} - 7 y^{4})

Solution steps

\frac{\partial}{\partial x} (sin (7 x^{5} y - 7 x y^{4}))

Treat

y

as a constant

Apply the chain rule:

cos (7 x^{5} y - 7 x y^{4}) \frac{\partial}{\partial x} (7 x^{5} y - 7 x y^{4})

= cos (7 x^{5} y - 7 x y^{4}) \frac{\partial}{\partial x} (7 x^{5} y - 7 x y^{4})

\frac{\partial}{\partial x} (7 x^{5} y - 7 x y^{4}) = 35 y x^{4} - 7 y^{4}

= cos (7 x^{5} y - 7 x y^{4}) (35 y x^{4} - 7 y^{4})

x \to 0 + lim (\frac{6}{x} - \frac{6}{∣ x ∣})

\int \frac{1}{a + x} d x

\int_{0}^{2} - x^{2} - x + 13 d x

\int (π - x) sin (n x) d x

(\frac{1 - 2 ln ( x )}{x ^{3}})^{^{'}}

What is (\partial)/(\partial x)(sin(7x^5y-7xy^4)) ?
The answer to (\partial)/(\partial x)(sin(7x^5y-7xy^4)) is cos(7x^5y-7xy^4)(35yx^4-7y^4)