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)}

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derivative of

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

- 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)}

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)}