What is (\partial)/(\partial x)(5x^4y^7+4x^8y^6) ?

The answer to (\partial)/(\partial x)(5x^4y^7+4x^8y^6) is 20y^7x^3+32y^6x^7

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(\partial)/(\partial x)(5x^4y^7+4x^8y^6)

\frac{\partial}{\partial x} (5 x^{4} y^{7} + 4 x^{8} y^{6})

20 y^{7} x^{3} + 32 y^{6} x^{7}

Solution steps

\frac{\partial}{\partial x} (5 x^{4} y^{7} + 4 x^{8} y^{6})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{4} y^{7}) + \frac{\partial}{\partial x} (4 x^{8} y^{6})

\frac{\partial}{\partial x} (5 x^{4} y^{7}) = 20 y^{7} x^{3}

\frac{\partial}{\partial x} (4 x^{8} y^{6}) = 32 y^{6} x^{7}

= 20 y^{7} x^{3} + 32 y^{6} x^{7}

sin (4 θ)

\int a x d x

\int x \cdot sin (\frac{nπ x}{2}) d x

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

\int 3 x sin (x^{2}) d x

What is (\partial)/(\partial x)(5x^4y^7+4x^8y^6) ?
The answer to (\partial)/(\partial x)(5x^4y^7+4x^8y^6) is 20y^7x^3+32y^6x^7