What is the derivative of-cos(e^x) ?

The derivative of-cos(e^x) is e^xsin(e^x)

What is the first derivative of-cos(e^x) ?

The first derivative of-cos(e^x) is e^xsin(e^x)

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\frac{d}{d x} (- cos (e^{x}))

e^{x} sin (e^{x})

Solution steps

\frac{d}{d x} (- cos (e^{x}))

Take the constant out:

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

= - \frac{d}{d x} (cos (e^{x}))

Apply the chain rule:

- sin (e^{x}) \frac{d}{d x} (e^{x})

= - sin (e^{x}) \frac{d}{d x} (e^{x})

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

= - (- sin (e^{x}) e^{x})

Simplify

= e^{x} sin (e^{x})

\int_{1}^{6} \frac{1}{2 x + 3 + x} d x

\frac{d}{d x} (7 x (x^{3} - 8 x + 2))

x \frac{d y}{d x} - 2 y = 5 x^{3}

\frac{\partial}{\partial x} (\frac{x ^{2}}{sin ^{2} ( x )})

\frac{\partial}{\partial z} (\frac{( x + y )}{y + z})

What is the derivative of-cos(e^x) ?
The derivative of-cos(e^x) is e^xsin(e^x)
What is the first derivative of-cos(e^x) ?
The first derivative of-cos(e^x) is e^xsin(e^x)