# Differentiating Exponential Functions with Other Bases

Distinguishing exponential functions with bases other than the standard 'e' involves a nuanced exploration of mathematical principles. While the base 'e' often takes precedence, various scenarios arise where different bases come into play, necessitating a specialized approach to differentiation. This subject delves into the techniques required to compute derivatives for exponential functions with bases beyond 'e,' elucidating the intricacies associated with non-standard bases. Such differentiation is fundamental in mathematical modeling and various scientific applications, making a precise understanding of these methods crucial for those navigating advanced calculus and mathematical analysis.

- How do you find the derivative of #y=3^sqrtx#?
- What is the derivative of #f(x)=b^x# ?
- What is the derivative of #f(x)= 2^(3x)#?
- What is the derivative of # 5^x#?
- How do you differentiate #y=x^(x-1)#?
- How do you differentiate #y = x ^ sqrt(x)#?
- How do you find the derivative of #g(alpha)=5^(-alpha/2)sin2alpha#?
- How do you differentiate #((e^x)+x)^(1/x)#?
- How do you differentiate #t(x)= 3^(7x-3)#?
- How do you find the equation of the tangent line to the graph #y=log_3x# through point (27,3)?
- How do you differentiate #y=x^(8x)#?
- How do you differentiate #9^x#?
- How do you find the derivative of #h(theta)=2^(-theta)cospitheta#?
- How do you differentiate #y=(1+x)^(1/x)#?
- How do you find the derivative of #g(t)=(10log_4t)/t#?
- How do you use logarithmic differentiation to find the derivative of #y=(cosx)^x#?
- How do you find the derivative of #g(t)=t^2 2^t#?
- How do you find the equation of the tangent line to the graph #y=2^-x# through point (-1,2)?
- How do you find the derivative of #y=2^(-3/x)#?
- How do you find the derivative of #2^xln2#?