What is (\partial)/(\partial x)(x^7+xy^9+1) ?

The answer to (\partial)/(\partial x)(x^7+xy^9+1) is 7x^6+y^9

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(\partial)/(\partial x)(x^7+xy^9+1)

\frac{\partial}{\partial x} (x^{7} + x y^{9} + 1)

7 x^{6} + y^{9}

Solution steps

\frac{\partial}{\partial x} (x^{7} + x y^{9} + 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{7}) + \frac{\partial}{\partial x} (x y^{9}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (x^{7}) = 7 x^{6}

\frac{\partial}{\partial x} (x y^{9}) = y^{9}

\frac{\partial}{\partial x} (1) = 0

= 7 x^{6} + y^{9} + 0

Simplify

= 7 x^{6} + y^{9}

\frac{d}{d x} (27 arctan (x))

\frac{\partial}{\partial x} (x^{2} + x y + 3 x + 2 y + 5)

y^{^{''}} + 4 y^{^{'}} + 4 y = - 3 e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

\frac{\partial}{\partial x} (x^{2} + y^{2} - 1)

f (x) = x^{3} - 7 x^{2} - 7 x + 4

What is (\partial)/(\partial x)(x^7+xy^9+1) ?
The answer to (\partial)/(\partial x)(x^7+xy^9+1) is 7x^6+y^9