What is (\partial)/(\partial y)(3x^2(5x+7y)) ?

The answer to (\partial)/(\partial y)(3x^2(5x+7y)) is 21x^2

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(\partial)/(\partial y)(3x^2(5x+7y))

\frac{\partial}{\partial y} (3 x^{2} (5 x + 7 y))

21 x^{2}

Solution steps

\frac{\partial}{\partial y} (3 x^{2} (5 x + 7 y))

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 x^{2} \frac{\partial}{\partial y} (5 x + 7 y)

Apply the Sum/Difference Rule:

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

= 3 x^{2} (\frac{\partial}{\partial y} (5 x) + \frac{\partial}{\partial y} (7 y))

\frac{\partial}{\partial y} (5 x) = 0

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

= 3 x^{2} (0 + 7)

Simplify

= 21 x^{2}

f (x) = x^{3} - 6 x^{2} + 9 x

x \to \frac{π}{4} lim (tan (2 x))

\int \frac{7 x + 3}{x} d x

x \to \infty lim (x^{4})

cos (k t)

What is (\partial)/(\partial y)(3x^2(5x+7y)) ?
The answer to (\partial)/(\partial y)(3x^2(5x+7y)) is 21x^2