What is (\partial)/(\partial x)(4x^2+y^2-7y) ?

The answer to (\partial)/(\partial x)(4x^2+y^2-7y) is 8x

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(\partial)/(\partial x)(4x^2+y^2-7y)

\frac{\partial}{\partial x} (4 x^{2} + y^{2} - 7 y)

8 x

Solution steps

\frac{\partial}{\partial x} (4 x^{2} + y^{2} - 7 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{2}) + \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (7 y)

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

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

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

= 8 x + 0 - 0

Simplify

= 8 x

\frac{d}{d x} (\frac{6 x}{x ^{2} + 3})

\frac{d}{d x} (\frac{1}{( x ^{3} + 9 ) ^{5}})

\frac{d}{d x} (sec^{2} (3 - 2 x))

x^{2} - 1

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

What is (\partial)/(\partial x)(4x^2+y^2-7y) ?
The answer to (\partial)/(\partial x)(4x^2+y^2-7y) is 8x