What is (\partial)/(\partial x)(3x^4+5x^4+9xy) ?

The answer to (\partial)/(\partial x)(3x^4+5x^4+9xy) is 32x^3+9y

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(\partial)/(\partial x)(3x^4+5x^4+9xy)

\frac{\partial}{\partial x} (3 x^{4} + 5 x^{4} + 9 x y)

32 x^{3} + 9 y

Solution steps

\frac{\partial}{\partial x} (3 x^{4} + 5 x^{4} + 9 x y)

Simplify

3 x^{4} + 5 x^{4} + 9 x y : 8 x^{4} + 9 x y

= \frac{\partial}{\partial x} (8 x^{4} + 9 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x^{4}) + \frac{\partial}{\partial x} (9 x y)

\frac{\partial}{\partial x} (8 x^{4}) = 32 x^{3}

\frac{\partial}{\partial x} (9 x y) = 9 y

= 32 x^{3} + 9 y

\frac{\partial}{\partial s} (\frac{7}{s})

h (x) = x^{3} + 4 x^{4}

f (t) = sin (2 t)

0.04 t^{3} - 0.12 t^{2}

What is (\partial)/(\partial x)(3x^4+5x^4+9xy) ?
The answer to (\partial)/(\partial x)(3x^4+5x^4+9xy) is 32x^3+9y