What is (\partial)/(\partial y)(y^6cos(5x)) ?

The answer to (\partial)/(\partial y)(y^6cos(5x)) is 6y^5cos(5x)

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(\partial)/(\partial y)(y^6cos(5x))

\frac{\partial}{\partial y} (y^{6} cos (5 x))

6 y^{5} cos (5 x)

Solution steps

\frac{\partial}{\partial y} (y^{6} cos (5 x))

Treat

x

as a constant

Take the constant out:

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

= cos (5 x) \frac{\partial}{\partial y} (y^{6})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= cos (5 x) \cdot 6 y^{6 - 1}

Simplify

= 6 y^{5} cos (5 x)

\int_{1}^{2} \frac{7 x - 2}{3 x ^{2} - 2 x} d x

f (x) = (4 x + 3) (- x + 1), at x = 4

\frac{d}{d x} (\frac{6}{4 x})

f (x) = 7 x - x^{2}, (1, 6)

\int_{- 1}^{1} \frac{1}{x} d x

What is (\partial)/(\partial y)(y^6cos(5x)) ?
The answer to (\partial)/(\partial y)(y^6cos(5x)) is 6y^5cos(5x)