What is (\partial)/(\partial x)(x^3y^5-2x^2y+x) ?

The answer to (\partial)/(\partial x)(x^3y^5-2x^2y+x) is 3y^5x^2-4yx+1

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(\partial)/(\partial x)(x^3y^5-2x^2y+x)

\frac{\partial}{\partial x} (x^{3} y^{5} - 2 x^{2} y + x)

3 y^{5} x^{2} - 4 y x + 1

Solution steps

\frac{\partial}{\partial x} (x^{3} y^{5} - 2 x^{2} y + x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{3} y^{5}) - \frac{\partial}{\partial x} (2 x^{2} y) + \frac{\partial}{\partial x} (x)

\frac{\partial}{\partial x} (x^{3} y^{5}) = 3 y^{5} x^{2}

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

\frac{\partial}{\partial x} (x) = 1

= 3 y^{5} x^{2} - 4 y x + 1

\int_{0}^{2} (x^{3} - 3 x^{2} + 2 x) d x

\frac{d}{d x} (csc (\frac{ln ( x + 3 )}{x ^{2}}))

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

\int \frac{( 3 x ^{2} - x + 2 e )}{x ^{2}} d x

\int \frac{x}{5 - x ^{2}} d x

What is (\partial)/(\partial x)(x^3y^5-2x^2y+x) ?
The answer to (\partial)/(\partial x)(x^3y^5-2x^2y+x) is 3y^5x^2-4yx+1