What is (\partial)/(\partial x)(10xcos(4xy)) ?

The answer to (\partial)/(\partial x)(10xcos(4xy)) is 10(cos(4xy)-4xysin(4xy))

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(\partial)/(\partial x)(10xcos(4xy))

\frac{\partial}{\partial x} (10 x cos (4 x y))

10 (cos (4 x y) - 4 x y sin (4 x y))

Solution steps

\frac{\partial}{\partial x} (10 x cos (4 x y))

Treat

y

as a constant

Take the constant out:

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

= 10 \frac{\partial}{\partial x} (x cos (4 x y))

Apply the Product Rule:

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

f = x, g = cos (4 x y)

= 10 (\frac{\partial}{\partial x} (x) cos (4 x y) + \frac{\partial}{\partial x} (cos (4 x y)) x)

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

\frac{\partial}{\partial x} (cos (4 x y)) = - sin (4 x y) \cdot 4 y

= 10 (1 \cdot cos (4 x y) + (- sin (4 x y) \cdot 4 y) x)

Simplify

= 10 (cos (4 x y) - 4 x y sin (4 x y))

x \to 0 lim (\frac{( x + 1 ) ^{4} - 1}{x})

\int x sin (x^{2} + 4) d x

x \frac{d y}{d x} - 2 y = 6 x^{5}

y^{^{''}} + 6 y^{^{'}} + 9 y = 18 t^{2} + 24 t + 4

f (x) = \frac{1}{x + 5}

What is (\partial)/(\partial x)(10xcos(4xy)) ?
The answer to (\partial)/(\partial x)(10xcos(4xy)) is 10(cos(4xy)-4xysin(4xy))