What is the derivative of x^3sin(1/x) ?

The derivative of x^3sin(1/x) is 3x^2sin(1/x)-xcos(1/x)

What is the first derivative of x^3sin(1/x) ?

The first derivative of x^3sin(1/x) is 3x^2sin(1/x)-xcos(1/x)

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\frac{d}{d x} (x^{3} sin (\frac{1}{x}))

3 x^{2} sin (\frac{1}{x}) - x cos (\frac{1}{x})

Solution steps

\frac{d}{d x} (x^{3} sin (\frac{1}{x}))

Apply the Product Rule:

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

f = x^{3}, g = sin (\frac{1}{x})

= \frac{d}{d x} (x^{3}) sin (\frac{1}{x}) + \frac{d}{d x} (sin (\frac{1}{x})) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (sin (\frac{1}{x})) = - \frac{cos ( \frac{1}{x} )}{x ^{2}}

= 3 x^{2} sin (\frac{1}{x}) + (- \frac{cos ( \frac{1}{x} )}{x ^{2}}) x^{3}

Simplify

3 x^{2} sin (\frac{1}{x}) + (- \frac{cos ( \frac{1}{x} )}{x ^{2}}) x^{3} : 3 x^{2} sin (\frac{1}{x}) - x cos (\frac{1}{x})

= 3 x^{2} sin (\frac{1}{x}) - x cos (\frac{1}{x})

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

f (x) = \frac{2 - 5 x}{e ^{x}}

x \to \infty lim (5^{x})

\frac{x}{2 + x}

\frac{\partial}{\partial x} (3 x y^{2} z^{3} - x yz)

What is the derivative of x^3sin(1/x) ?
The derivative of x^3sin(1/x) is 3x^2sin(1/x)-xcos(1/x)
What is the first derivative of x^3sin(1/x) ?
The first derivative of x^3sin(1/x) is 3x^2sin(1/x)-xcos(1/x)