d dx sin(x2) = 2x cos(x2) Same result as before (thank goodness!)Another couple of examples of the Chain Rule:Example: What is ddx(1/cos(x)) ? 1/cos(x) is made up of 1/g and cos(): f(g) = 1/g g(x) = cos(x) The Chain Rule says: the derivative of f(g(x)) ...
The derivative off(x)=x2+2xatx=2is View Solution The derivative off(x)=2√x−1xis View Solution The anti - derivative off(x)=ex/2whose graph passes through the point (0,3) is : View Solution Free Ncert Solutions English Medium ...
What is the derivative of (e−2x)(cosx)? Differentiation in calculus: Derivative gives how fast your function is changing at any point on the graph. There are many techniques to find the derivative of a function. These techniques are used to make the differential process easier. In this ...
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=1x. It is an interesting result that ...
Step by step video & image solution for Find the derivative of y = log (e^(2x)). by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams. Updated on:21/07/2023 Class 12MATHSCONTINUITY AND DIFFERENTIABILITY ...
Answer to: Find the derivative of: f (x)= sech (e^{2x}) By signing up, you'll get thousands of step-by-step solutions to your homework questions...
例: (eax)′=a⋅eax ; (lnx2)′=1x2⋅2x 高阶导数的运算 (x^{a})^{(n)}=x^{a-n} \prod_{k=0}^{n-1} (a-k) (\frac{1}{x})^{(n)}=(-1)^n\frac{n!}{x^{n+1}} \quad\quad (n=1,2,...)(\ln x)^{(n)}=(-1)^{(n-1)}\frac{(n-1)!}{x^{n}...
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. ...
A。解析:首先求一阶导数,设\(u = x^{2}\),\(y = e^{u}\),根据复合函数求导法则\(y^\prime=e^{u}\times u^\prime\),\(u^\prime = 2x\),所以\(y^\prime = 2xe^{x^{2}}\)。再求二阶导数,\(y^{\prime\prime}=2e^{x^{2}}+2x\times2xe^{x^{2}}=2e^{x^{2}}(2x^{...
A. Find the derivative of the function. y = (x^2 - 4x + 4)e^7 \frac{x}{4} B. Find the derivative of the function. y = (2x + 3)^5(5x + 1)^{-3} 1. Find the derivative of the function. f(x) = x^4 \sqrt{1-4x} 2. Find the derivative of the function....