What is the derivative of y=x^2cos(4/x) ?

The derivative of y=x^2cos(4/x) is 2xcos(4/x)+4sin(4/x)

What is the first derivative of y=x^2cos(4/x) ?

The first derivative of y=x^2cos(4/x) is 2xcos(4/x)+4sin(4/x)

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derivative of

y = x^{2} cos (\frac{4}{x})

2 x cos (\frac{4}{x}) + 4 sin (\frac{4}{x})

Solution steps

\frac{d}{d x} (x^{2} cos (\frac{4}{x}))

Apply the Product Rule:

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

f = x^{2}, g = cos (\frac{4}{x})

= \frac{d}{d x} (x^{2}) cos (\frac{4}{x}) + \frac{d}{d x} (cos (\frac{4}{x})) x^{2}

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

\frac{d}{d x} (cos (\frac{4}{x})) = \frac{4 sin ( \frac{4}{x} )}{x ^{2}}

= 2 x cos (\frac{4}{x}) + \frac{4 sin ( \frac{4}{x} )}{x ^{2}} x^{2}

\frac{4 sin ( \frac{4}{x} )}{x ^{2}} x^{2} = 4 sin (\frac{4}{x})

= 2 x cos (\frac{4}{x}) + 4 sin (\frac{4}{x})

f (x) = x^{4} + 2 e^{x}, (0, 2)

(sin (x))^{2}

x \to 0 + lim (- x + 5)

e^{- 3 x}

x \to 9 - lim (\frac{x ^{9}}{x - 9})

What is the derivative of y=x^2cos(4/x) ?
The derivative of y=x^2cos(4/x) is 2xcos(4/x)+4sin(4/x)
What is the first derivative of y=x^2cos(4/x) ?
The first derivative of y=x^2cos(4/x) is 2xcos(4/x)+4sin(4/x)