What is (\partial)/(\partial x)(3x^4y^5+5x^7y^8) ?

The answer to (\partial)/(\partial x)(3x^4y^5+5x^7y^8) is 12y^5x^3+35y^8x^6

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(\partial)/(\partial x)(3x^4y^5+5x^7y^8)

\frac{\partial}{\partial x} (3 x^{4} y^{5} + 5 x^{7} y^{8})

12 y^{5} x^{3} + 35 y^{8} x^{6}

Solution steps

\frac{\partial}{\partial x} (3 x^{4} y^{5} + 5 x^{7} y^{8})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x^{4} y^{5}) + \frac{\partial}{\partial x} (5 x^{7} y^{8})

\frac{\partial}{\partial x} (3 x^{4} y^{5}) = 12 y^{5} x^{3}

\frac{\partial}{\partial x} (5 x^{7} y^{8}) = 35 y^{8} x^{6}

= 12 y^{5} x^{3} + 35 y^{8} x^{6}

\int_{0}^{3} \frac{1}{x - 1} d x

f (x) = - 2 x^{3}, (- 1, 2)

\frac{9}{( s + 3 ) ^{3}}

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

y^{^{'}} + \frac{1}{x} y = 3 x^{2}

What is (\partial)/(\partial x)(3x^4y^5+5x^7y^8) ?
The answer to (\partial)/(\partial x)(3x^4y^5+5x^7y^8) is 12y^5x^3+35y^8x^6