What is (\partial)/(\partial x)(sin(x^2)+xy^3) ?

The answer to (\partial)/(\partial x)(sin(x^2)+xy^3) is cos(x^2)*2x+y^3

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(\partial)/(\partial x)(sin(x^2)+xy^3)

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

cos (x^{2}) \cdot 2 x + y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (sin (x^{2})) = cos (x^{2}) \cdot 2 x

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

= cos (x^{2}) \cdot 2 x + y^{3}

f (x) = \frac{1 + csc ( x ^{3} )}{1 - cot ( x ^{3} )}

\int (4 - x)^{3} d x

n = 1 \sum \infty \frac{n ^{2}}{n + 1}

y = - \frac{x}{9 y}

\frac{d}{d t} (- 4 t^{2} + 176 t + 100)

What is (\partial)/(\partial x)(sin(x^2)+xy^3) ?
The answer to (\partial)/(\partial x)(sin(x^2)+xy^3) is cos(x^2)*2x+y^3