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

The answer to (\partial)/(\partial x)(3xsin(7x^2y)) is 3(sin(7x^2y)+14x^2ycos(7x^2y))

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(\partial)/(\partial x)(3xsin(7x^2y))

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

3 (sin (7 x^{2} y) + 14 x^{2} y cos (7 x^{2} y))

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = sin (7 x^{2} y)

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

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

\frac{\partial}{\partial x} (sin (7 x^{2} y)) = cos (7 x^{2} y) \cdot 14 y x

= 3 (1 \cdot sin (7 x^{2} y) + cos (7 x^{2} y) \cdot 14 y xx)

Simplify

3 (1 \cdot sin (7 x^{2} y) + cos (7 x^{2} y) \cdot 14 y xx) : 3 (sin (7 x^{2} y) + 14 x^{2} y cos (7 x^{2} y))

= 3 (sin (7 x^{2} y) + 14 x^{2} y cos (7 x^{2} y))

\frac{\partial}{\partial x} (x e^{y} - y e^{x})

\int_{0}^{1} \frac{3 ^{3 x} - 1}{3 ^{x}} d x

y = (2 x + 1) + \frac{2}{( 2 x + 1 ) ^{3}}

\int_{- 1}^{1} x (1 - x)^{2} d x

x \to 0 + lim (\frac{1}{sin ^{2} ( x )})

What is (\partial)/(\partial x)(3xsin(7x^2y)) ?
The answer to (\partial)/(\partial x)(3xsin(7x^2y)) is 3(sin(7x^2y)+14x^2ycos(7x^2y))