Find the Derivative - d/dr pe^(rt)

Problem

(d(p)*e(r*t))/d(r)

Solution

1. Identify the variable of differentiation, which is r

2. Treat the variables p and t as constants with respect to r

3. Apply the constant multiple rule by moving the constant p outside the derivative.

(d(p)*e(r*t))/d(r)=pd(e(r*t))/d(r)

4. Apply the chain rule for the exponential function, where the derivative of eu is eud(u)/d(r)

d(e(r*t))/d(r)=e(r*t)(d(r)*t)/d(r)

5. Differentiate the exponent r*t with respect to r which results in t

(d(r)*t)/d(r)=t

6. Combine the results to find the final derivative.

p⋅e(r*t)⋅t=p*t*e(r*t)

Final Answer

(d(p)*e(r*t))/d(r)=p*t*e(r*t)

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