How do you find the derivative of f(x)=7^(2x)? Calculus Basic Differentiation Rules Chain Rule 1 Answer Barry H. Apr 3, 2018 ln49[7^[2x]] Explanation: By the theory of logs 7^[2x can be written as e^[2xln7] ,i.e, 7^[2x]=e^[2xln7].....[1] Therefore, d/dx7^[2x= d/[dx][e^[2xln7]] d/dx[e^[2xln7]]=[e^[2xln7]d/dx[2xln7]] and since ln7 is a constant, d/dx[2xln7] = 2ln7..... So, d/dx7^[2x=2ln7[e^[2xln7]].......[2] From .....[1], e^[2xln7= 7^[2x so substituting in 2, d/dx 7^[2x=2ln7[7^[2x]]=ln49[7^[2x]]. Hope this was helpful. Answer link Related questions What is the Chain Rule for derivatives? How do you find the derivative of y= 6cos(x^2) ? How do you find the derivative of y=6 cos(x^3+3) ? How do you find the derivative of y=e^(x^2) ? How do you find the derivative of y=ln(sin(x)) ? How do you find the derivative of y=ln(e^x+3) ? How do you find the derivative of y=tan(5x) ? How do you find the derivative of y= (4x-x^2)^10 ? How do you find the derivative of y= (x^2+3x+5)^(1/4) ? How do you find the derivative of y= ((1+x)/(1-x))^3 ? See all questions in Chain Rule Impact of this question 6056 views around the world You can reuse this answer Creative Commons License