the derivative of f(g(x)) = f’(g(x))g’(x) The individual derivatives are: f'(g) = −1/(g2) g'(x) = −sin(x) So: (1/cos(x))’ =−1g(x)2(−sin(x)) =sin(x)cos2(x) Note:sin(x)cos2(x)is alsotan(x)cos(x)or many other forms. ...
试题来源: 解析 let fixi-tans f(x+h)=tan(x+h) From the dffnition, f'(x)=ln((1/n))-(f(x+h)-f(x))/h = tanuthi-canky lìn h~0 h 、二 h sinh 二 ? ()) 1)()[()=1 s, f'(x)=tanx,f'(x)=sin^2x 反馈 收藏 ...
Answer to: Find the derivative of y = (tan x)^{ln x} By signing up, you'll get thousands of step-by-step solutions to your homework questions. You...
Find the 32th derivative of y=cos(2x). Higher order derivatives: The derivative of cos(x) is -sin(x). The derivative of (-sin x) is -cos(x). That is, these two functions will alternate (barring the sign change) as we keep taking the derivative of it. Hence we do not need...
Finding the derivative of other powers of e can than be done by using the chain rule. For example e2x^2is a function of the form f(g(x)) where f(x) = exand g(x) = 2x2. The derivative following the chain rule then becomes 4x e2x^2. ...
Transcribed Image Text:**Find the derivative of:** \[ f(x) = 3^{2x} (x^2 + 5) \tan(5x) \] --- **Explanation:** This function involves a combination of exponential, polynomial, and trigonometric components. To find the derivative, apply the product rule, ...
The derivative formula and the proof here will enumerate the derivatives of five basic elementary functions and their derivation process (elementary function can be calculated by it): basic derivative formula 1. constant function (i.e. constant) y=c (C constant) y'=0 2. power function y=x^...
Use the second derivative to determine the point of inflection for {eq}y = x^3 + x^2 + 8x + 12 {/eq}. Inflection Points and Concavity: A function {eq}\displaystyle{ \begin{align} f \end{align} } {/eq} is said to be concave up (or down) at a point {eq}\displays...
Find the derivative y' of y = 8t^3 - 4t^2 + 12t - 3. Find the derivative y = \frac{\ln(9x + 7)}{e^{9x + 7 Find the derivative: y= \frac{\tan x-2}{\sec x}. Find the derivative. f(t) = te^{- 6t} f '(t) = Find the derivative of ((2x+1)^{-1...
What is the derivative off(x)=xln(x)? Differentiation This question is from the differentiation and we have to find out the first-order derivative of the given function. We will use the product rule to solve this. The product rule is given below ...