What is the derivative of 2e^{cos(x/2}) ?

The derivative of 2e^{cos(x/2}) is -e^{cos(x/2)}sin(x/2)

What is the first derivative of 2e^{cos(x/2}) ?

The first derivative of 2e^{cos(x/2}) is -e^{cos(x/2)}sin(x/2)

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\frac{d}{d x} (2 e^{c o s (\frac{x}{2})})

- e^{c o s (\frac{x}{2})} sin (\frac{x}{2})

Solution steps

\frac{d}{d x} (2 e^{c o s (\frac{x}{2})})

Take the constant out:

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

= 2 \frac{d}{d x} (e^{c o s (\frac{x}{2})})

Apply the chain rule:

e^{c o s (\frac{x}{2})} \frac{d}{d x} (cos (\frac{x}{2}))

= e^{c o s (\frac{x}{2})} \frac{d}{d x} (cos (\frac{x}{2}))

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

= 2 e^{c o s (\frac{x}{2})} (- sin (\frac{x}{2}) \frac{1}{2})

Simplify

2 e^{c o s (\frac{x}{2})} (- sin (\frac{x}{2}) \frac{1}{2}) : - e^{c o s (\frac{x}{2})} sin (\frac{x}{2})

= - e^{c o s (\frac{x}{2})} sin (\frac{x}{2})

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

\int \frac{2 x + 1}{x ^{2} - x - 6} d x

\int 4 sech (x) tanh (x) d x

x \to 0 lim (2 x^{3})

\frac{d y}{d x} = 1 + x - y - x y

What is the derivative of 2e^{cos(x/2}) ?
The derivative of 2e^{cos(x/2}) is -e^{cos(x/2)}sin(x/2)
What is the first derivative of 2e^{cos(x/2}) ?
The first derivative of 2e^{cos(x/2}) is -e^{cos(x/2)}sin(x/2)