What is the derivative of f(x)=-(xsin((x^2)/4))/(2) ?

The derivative of f(x)=-(xsin((x^2)/4))/(2) is -1/2 (sin((x^2)/4)+(x^2cos((x^2)/4))/(2))

What is the first derivative of f(x)=-(xsin((x^2)/4))/(2) ?

The first derivative of f(x)=-(xsin((x^2)/4))/(2) is -1/2 (sin((x^2)/4)+(x^2cos((x^2)/4))/(2))

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derivative of

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

- \frac{1}{2} sin (\frac{x ^{2}}{4}) + \frac{x ^{2} cos ( \frac{x ^{2}}{4} )}{2}

Solution steps

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

Take the constant out:

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

= - \frac{1}{2} \frac{d}{d x} (x sin (\frac{x ^{2}}{4}))

Apply the Product Rule:

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

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

= - \frac{1}{2} (\frac{d x}{d x} sin (\frac{x ^{2}}{4}) + \frac{d}{d x} (sin (\frac{x ^{2}}{4})) x)

\frac{d x}{d x} = 1

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

= - \frac{1}{2} 1 \cdot sin (\frac{x ^{2}}{4}) + \frac{x cos ( \frac{x ^{2}}{4} )}{2} x

Simplify

- \frac{1}{2} 1 \cdot sin (\frac{x ^{2}}{4}) + \frac{x cos ( \frac{x ^{2}}{4} )}{2} x : - \frac{1}{2} sin (\frac{x ^{2}}{4}) + \frac{x ^{2} cos ( \frac{x ^{2}}{4} )}{2}

= - \frac{1}{2} sin (\frac{x ^{2}}{4}) + \frac{x ^{2} cos ( \frac{x ^{2}}{4} )}{2}

\int e^{x} 11 + e^{x} d x

104 - 80 e^{- 0.2 t}

arcsin (2 x + 1)

\int e^{(- \frac{x ^{2}}{4})} d x

\frac{d y}{d t} = \frac{t}{y - 2}

What is the derivative of f(x)=-(xsin((x^2)/4))/(2) ?
The derivative of f(x)=-(xsin((x^2)/4))/(2) is -1/2 (sin((x^2)/4)+(x^2cos((x^2)/4))/(2))
What is the first derivative of f(x)=-(xsin((x^2)/4))/(2) ?
The first derivative of f(x)=-(xsin((x^2)/4))/(2) is -1/2 (sin((x^2)/4)+(x^2cos((x^2)/4))/(2))