What is (\partial)/(\partial x)(12y^5x^3+35y^8x^6) ?

The answer to (\partial)/(\partial x)(12y^5x^3+35y^8x^6) is 36y^5x^2+210y^8x^5

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(\partial)/(\partial x)(12y^5x^3+35y^8x^6)

\frac{\partial}{\partial x} (12 y^{5} x^{3} + 35 y^{8} x^{6})

36 y^{5} x^{2} + 210 y^{8} x^{5}

Solution steps

\frac{\partial}{\partial x} (12 y^{5} x^{3} + 35 y^{8} x^{6})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (12 y^{5} x^{3}) + \frac{\partial}{\partial x} (35 y^{8} x^{6})

\frac{\partial}{\partial x} (12 y^{5} x^{3}) = 36 y^{5} x^{2}

\frac{\partial}{\partial x} (35 y^{8} x^{6}) = 210 y^{8} x^{5}

= 36 y^{5} x^{2} + 210 y^{8} x^{5}

6 (t + 1) \frac{d y}{d t} - 5 y = 5 t

x \to 0 lim (\frac{( x ^{2} - 2 )}{x})

\frac{d}{d x} (x^{4} + y^{4} + z^{4} - 4 x y z)

\int \frac{x}{x - 3} d x

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

What is (\partial)/(\partial x)(12y^5x^3+35y^8x^6) ?
The answer to (\partial)/(\partial x)(12y^5x^3+35y^8x^6) is 36y^5x^2+210y^8x^5