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Popular >

derivative of e^{(cos(t)+ln(t))}

Solution

derivative of

e^{(c o s (t) + l n (t))}

Solution

- e^{c o s (t)} t sin (t) + e^{c o s (t)}

Solution steps

\frac{d}{d t} (e^{c o s (t) + l n (t)})

Simplify

e^{c o s (t) + l n (t)} : e^{c o s (t)} t

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

Apply the Product Rule:

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

f = e^{c o s (t)}, g = t

= \frac{d}{d t} (e^{c o s (t)}) t + \frac{d t}{d t} e^{c o s (t)}

\frac{d}{d t} (e^{c o s (t)}) = - e^{c o s (t)} sin (t)

\frac{d t}{d t} = 1

= (- e^{c o s (t)} sin (t)) t + 1 \cdot e^{c o s (t)}

Simplify

= - e^{c o s (t)} t sin (t) + e^{c o s (t)}

Popular Examples

(\partial)/(\partial x)(e^{t-x}+e^{w-1})

\frac{\partial}{\partial x} (e^{t - x} + e^{w - 1})

integral of cos(6x)cos(5x)

\int cos (6 x) cos (5 x) d x

derivative of g(t)=(t-sqrt(t))/(t^{1/5)}derivative of

g (t) = \frac{t - t}{t ^{\frac{1}{5}}}

(dy)/(dx)=((2cos(2x)))/(3+2y)

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

limit as x approaches infinity of 1/(2x)

x \to \infty lim (\frac{1}{2 x})

Frequently Asked Questions (FAQ)

What is the derivative of e^{(cos(t)+ln(t))} ?
The derivative of e^{(cos(t)+ln(t))} is -e^{cos(t)}tsin(t)+e^{cos(t)}
What is the first derivative of e^{(cos(t)+ln(t))} ?
The first derivative of e^{(cos(t)+ln(t))} is -e^{cos(t)}tsin(t)+e^{cos(t)}