What is the derivative of e^{cos(sqrt(x+3)}) ?

The derivative of e^{cos(sqrt(x+3)}) is -(e^{cos(sqrt(x+3))}sin(sqrt(x+3)))/(2sqrt(x+3))

What is the first derivative of e^{cos(sqrt(x+3)}) ?

The first derivative of e^{cos(sqrt(x+3)}) is -(e^{cos(sqrt(x+3))}sin(sqrt(x+3)))/(2sqrt(x+3))

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\frac{d}{d x} (e^{c o s (x + 3)})

- \frac{e ^{c o s (x + 3)} sin ( x + 3 )}{2 x + 3}

Solution steps

\frac{d}{d x} (e^{c o s (x + 3)})

Apply the chain rule:

e^{c o s (x + 3)} \frac{d}{d x} (cos (x + 3))

= e^{c o s (x + 3)} \frac{d}{d x} (cos (x + 3))

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

= e^{c o s (x + 3)} (- \frac{sin ( x + 3 )}{2 x + 3})

Simplify

e^{c o s (x + 3)} (- \frac{sin ( x + 3 )}{2 x + 3}) : - \frac{e ^{c o s (x + 3)} sin ( x + 3 )}{2 x + 3}

= - \frac{e ^{c o s (x + 3)} sin ( x + 3 )}{2 x + 3}

- 8 t^{2} y^{^{''}} - 4 t (t - 4) y^{^{'}} + 4 (t - 4) y = 0

y^{2} = x, x - 2 y = 3

\frac{d}{d x} (3 x (x^{2} - x + 1) (5 x - 3))

\frac{d y}{d t} = - 2 y, y (0) = \frac{1}{10}

x^{2} - 8

What is the derivative of e^{cos(sqrt(x+3)}) ?
The derivative of e^{cos(sqrt(x+3)}) is -(e^{cos(sqrt(x+3))}sin(sqrt(x+3)))/(2sqrt(x+3))
What is the first derivative of e^{cos(sqrt(x+3)}) ?
The first derivative of e^{cos(sqrt(x+3)}) is -(e^{cos(sqrt(x+3))}sin(sqrt(x+3)))/(2sqrt(x+3))