Derivative of an Exponential Function: One of the structures of an exponential function iseu. The derivative of this function utilizes: ddxeu=euu′(x) We will utilize this twice as the function provided contains two functions of the formeu. ...
Then differentiate the power of the exponential function; this is done using the chain rule. Answer and Explanation: Given: The function is {eq}y = {e^{k\tan \sqrt x }}{/eq}. The objective is to find the derivative of the given function. Recall the......
Finding the derivative of a function is called differentiation. Basically, you calculate the slope of the line that goes throughfat the pointsxandx+h. Because we take the limit forhto 0, these points will lie infinitesimally close together; therefore, it is the slope of the function in the...
One of the important operations you do in calculus is finding derivatives. The derivative of a function is also called the rate of change of that function. For instance, if x(t) is the position of a car at any time t, then the derivative of x, which is written dx/dt, is the veloc...
Find the derivative: y=2ex+e−x A Derivative of Rational Function: In the provided equation, a rational number is there to the right side. In this rational number, a constant is in the numerator and the sum of two exponential functions is in the denominator. Division Rule of Derivative...
The derivative of an exponential function is always equal to the same function. Answer and Explanation:1 Simplifying the given exponential expression, we get: {eq}\begin{align*} \displaystyle \frac{d}{dx}[\frac{3e^x+8e^{-x}}{8}... ...
Section Summary Continued 4.1 Antidifferentiation Section Summary Continued The Constant Rule of Antidifferentiation is The Power Rule of Antidifferentiation is The Natural Logarithm Rule of Antidifferentiation is The Exponential Rule (base e) of Antidifferentiation is An initial condition is an ordered pair...
The product of the density and the derivative of the pressure once again comes out as space-invariable, \begin{aligned} \rho (x)&=p_{\text {in}}^{-1}\cdot {\left( \frac{p_{\text {out}}}{p_{\text {in}}}\right) }^{-\frac{x}{w}}\cdot \frac{p_0^2M}{RT_0},\nonumb...
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Is his absolute value function derivable at this point? Solution: remember that the derivative of the absolute value of a function is equal to f (x) divided by the absolute value (f (x)) and multiplied by the derivative of F (x). So the judgment of absolute value function is not ...