What is (\partial)/(\partial x)(7xcos(5xy)) ?

The answer to (\partial)/(\partial x)(7xcos(5xy)) is 7(cos(5xy)-5xysin(5xy))

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(\partial)/(\partial x)(7xcos(5xy))

\frac{\partial}{\partial x} (7 x cos (5 x y))

7 (cos (5 x y) - 5 x y sin (5 x y))

Solution steps

\frac{\partial}{\partial x} (7 x cos (5 x y))

Treat

y

as a constant

Take the constant out:

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

= 7 \frac{\partial}{\partial x} (x cos (5 x y))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos (5 x y)

= 7 (\frac{\partial}{\partial x} (x) cos (5 x y) + \frac{\partial}{\partial x} (cos (5 x y)) x)

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

\frac{\partial}{\partial x} (cos (5 x y)) = - sin (5 x y) \cdot 5 y

= 7 (1 \cdot cos (5 x y) + (- sin (5 x y) \cdot 5 y) x)

Simplify

= 7 (cos (5 x y) - 5 x y sin (5 x y))

x y y^{^{'}} = 4 x^{2} + 2 y^{2}

\frac{d}{d x} (x \cdot y^{2})

t^{\frac{5}{2}}

\int x^{4} e^{(x^{5})} d x

x \to 5 lim (\frac{x ^{2} + 1}{x - 5})

What is (\partial)/(\partial x)(7xcos(5xy)) ?
The answer to (\partial)/(\partial x)(7xcos(5xy)) is 7(cos(5xy)-5xysin(5xy))