Question

Найти производную показательной функции

Answer 1

$(a^{x})'=a^{x}\cdot lna\\\\a=21\; \; ,\; \; \; (-21^{x})'=-21^{x}\cdot ln21$

Answer 2

Derivative of an Exponential Function

To find the derivative of an exponential function, we can use the general rule for differentiating exponential functions. The derivative of an exponential function with base 'a' is given by:

y'(x) = (a^x) * ln(a)

Here, 'a' represents the base of the exponential function, and ln(a) represents the natural logarithm of the base.

For example, let's find the derivative of the function y(x) = 2^x:

Using the derivative rule, we have:

y'(x) = (2^x) * ln(2) Therefore, the derivative of the function y(x) = 2^x is y'(x) = (2^x) * ln(2).

Similarly, if we have a function like y(x) = 3 * π^x, we can find its derivative as follows:

y'(x) = (3 * π^x) * ln(π) So, the derivative of the function y(x) = 3 * π^x is y'(x) = (3 * π^x) * ln(π).

Please note that the derivative of an exponential function follows a general pattern, and the same rule can be applied to other exponential functions as well.

I hope this helps! Let me know if you have any further questions.