What is (\partial)/(\partial x)(3xy^6+sin(pix)-z) ?

The answer to (\partial)/(\partial x)(3xy^6+sin(pix)-z) is 3y^6+picos(pix)

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(\partial)/(\partial x)(3xy^6+sin(pix)-z)

\frac{\partial}{\partial x} (3 x y^{6} + sin (π x) - z)

3 y^{6} + π cos (π x)

Solution steps

\frac{\partial}{\partial x} (3 x y^{6} + sin (π x) - z)

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x y^{6}) + \frac{\partial}{\partial x} (sin (π x)) - \frac{\partial}{\partial x} (z)

\frac{\partial}{\partial x} (3 x y^{6}) = 3 y^{6}

\frac{\partial}{\partial x} (sin (π x)) = cos (π x) π

\frac{\partial}{\partial x} (z) = 0

= 3 y^{6} + cos (π x) π - 0

Simplify

= 3 y^{6} + π cos (π x)

\int x (6 x^{2} - x + 7) d x

x, x^{3} - 3 x^{2} + 3 x, - 0, 1

\frac{- 5 x}{2 x - 1}

e^{b x}

\int_{0}^{x} \frac{1}{x ^{2}} d x

What is (\partial)/(\partial x)(3xy^6+sin(pix)-z) ?
The answer to (\partial)/(\partial x)(3xy^6+sin(pix)-z) is 3y^6+picos(pix)