What is (\partial)/(\partial x)(x^4+x*sin(y)) ?

The answer to (\partial)/(\partial x)(x^4+x*sin(y)) is 4x^3+sin(y)

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(\partial)/(\partial x)(x^4+x*sin(y))

\frac{\partial}{\partial x} (x^{4} + x \cdot sin (y))

4 x^{3} + sin (y)

Solution steps

\frac{\partial}{\partial x} (x^{4} + x sin (y))

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

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

= 4 x^{3} + sin (y)

\int \frac{1}{x ( x - 2 )} d x

\int \frac{6400 q}{16 q ^{2} + 3200} d q

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

x \to 5 lim (3 x^{2} - 4 x - 1)

f (x) = 8 x + x^{2} + 7 x + 3

What is (\partial)/(\partial x)(x^4+x*sin(y)) ?
The answer to (\partial)/(\partial x)(x^4+x*sin(y)) is 4x^3+sin(y)