What is (\partial)/(\partial x)(2y^7+7y^9x^6) ?

The answer to (\partial)/(\partial x)(2y^7+7y^9x^6) is 42y^9x^5

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(\partial)/(\partial x)(2y^7+7y^9x^6)

\frac{\partial}{\partial x} (2 y^{7} + 7 y^{9} x^{6})

42 y^{9} x^{5}

Solution steps

\frac{\partial}{\partial x} (2 y^{7} + 7 y^{9} x^{6})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 y^{7}) + \frac{\partial}{\partial x} (7 y^{9} x^{6})

\frac{\partial}{\partial x} (2 y^{7}) = 0

\frac{\partial}{\partial x} (7 y^{9} x^{6}) = 42 y^{9} x^{5}

= 0 + 42 y^{9} x^{5}

Simplify

= 42 y^{9} x^{5}

\int 2 x (x + 1) d x

x \to 2 lim (x^{3} + 8)

\frac{d}{d x} (7 x arcsin (x))

\frac{200 t}{t + 2}

\int \frac{1}{( ln ( x ) ) ^{3} x} d x

What is (\partial)/(\partial x)(2y^7+7y^9x^6) ?
The answer to (\partial)/(\partial x)(2y^7+7y^9x^6) is 42y^9x^5