8-basic rule of derivative基础的求导规则 14:10 9-product rule and quotient rule乘法法则与商的法则 13:00 10-chain rule链式法则 23:06 11-second derivative二阶导函数 06:38 12-implicit differentiation隐微分 23:37 13-derivative of an inverse function反函数求导 19:19 14-derivative of ...
Derivative Of Inverse Trigonometric Functions | Examples 58:35 Find the derivative of the inverse function of the following: y= x^2 e... 01:15 Find the derivative of the inverse function of the following: y= x cos... 02:09 Find the derivative of the inverse function of the following:...
Answer to: Consider the following function. Without finding the inverse, evaluate the derivative of the inverse at the given point. f(x) = 3x + 4;...
Inverse functions: if f is one-to-one function with domain X and range Y and g is function with domain Y and range X then g is the inverse function of. 5.3 Inverse Functions. Definition of Inverse Function A function of “g” is the inverse function of the function “f” if: f(g(...
Derivative of Exponential Function Formula How to Find the Derivative of an Exponential Function Derivative of Exponential Function Examples Lesson SummaryWhat is an Exponential Function?What is an exponential function? Well, an exponential function is a function of the form {eq}f(x) = a^x {/eq...
Note that if {eq}(b,f(b)) {/eq} is a point of the function {eq}f(x) {/eq}, then {eq}(f(b),b) {/eq} is a point of the inverse, which is {eq}f^{-1}(x) {/eq}. Answer and Explanation: Using the formula {eq}\displaystyle \frac{\mathrm{d}}{\m...
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...
Now, practice with a few examples. Example 1: What is the derivative of ln(2x)? Notice that the chain rule can be used here to find the derivative. In this case, the inside function is 2x, and the outside function is ln(x). Therefore, ddxln(2x)=12x⋅ddx2x=12x⋅2=1...
Hence, we have derived the derivative of cos x using the quotient rule of differentiation.Anti-Derivative of cos xThe anti-derivative of cos x is nothing but the integral of cos x. As the name suggests, anti-derivative is the inverse process of differentiation. The derivative of cos x is...
For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization. A closely ...