What is (\partial)/(\partial x)(4x^4y^8+9x^6y^7) ?

The answer to (\partial)/(\partial x)(4x^4y^8+9x^6y^7) is 16y^8x^3+54y^7x^5

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(\partial)/(\partial x)(4x^4y^8+9x^6y^7)

\frac{\partial}{\partial x} (4 x^{4} y^{8} + 9 x^{6} y^{7})

16 y^{8} x^{3} + 54 y^{7} x^{5}

Solution steps

\frac{\partial}{\partial x} (4 x^{4} y^{8} + 9 x^{6} y^{7})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{4} y^{8}) + \frac{\partial}{\partial x} (9 x^{6} y^{7})

\frac{\partial}{\partial x} (4 x^{4} y^{8}) = 16 y^{8} x^{3}

\frac{\partial}{\partial x} (9 x^{6} y^{7}) = 54 y^{7} x^{5}

= 16 y^{8} x^{3} + 54 y^{7} x^{5}

\frac{d}{d x} (2^{x} (x^{2} + 1))

(2 x - 1) d x + (3 y + 5) d y = 0

\int (1 + 4 x)^{\frac{3}{5}} d x

\frac{\partial}{\partial x} (x sin (z))

x^{2} y^{^{'}} + 2 x y = e^{3 x}

What is (\partial)/(\partial x)(4x^4y^8+9x^6y^7) ?
The answer to (\partial)/(\partial x)(4x^4y^8+9x^6y^7) is 16y^8x^3+54y^7x^5