Find the derivative of the function. {eq}y = \dfrac{1}{2}x\sqrt{x^2 + a^2} + \dfrac{1}{2}a^2 \ln \ln \left(x + \sqrt{x^2 + a^2}\right) {/eq} Derivative of Logarithmic Functions: The logarithm of a neg...
The logarithmic functions are of either base e or of the different base. To find the derivative of the logarithmic functions, we need to have the log function with base e. This is the natural log function.Answer and Explanation: Become a Study.com member to unlock this answer! Cr...
There are many techniques to find the derivative of a function. To solve this problem, we'll apply logarithmic property logax=lnxlna and simplify the given function,. Then use the chain rule, which states that: df(u) dx= df du du dx. Next, use the common derivatives d ...
To isolate f′(x), we multiply both sides by f(x):f′(x)=f(x)⋅ln(a) Step 7: Substitute back the original functionNow we substitute back f(x)=ax:f′(x)=ax⋅ln(a) Final ResultThus, the derivative of the function f(x)=ax with respect to x is:f′(x)=axln(a) ---...
Use logarithmic differentiation to find the derivative of the function. y = (cos 2x)^x 求方程导数y=(cos2x)^x... 求方程导数y = (cos 2x)^x 展开 1个回答 #热议# 已婚女性就应该承担家里大部分家务吗?0A0小迷糊 2014-05-16 · TA获得超过1018个赞 知道小有建树答主 回答量:523 采纳率...
To find the derivative of the function Y=(x+1x)x+x(1+1x) with respect to x, we will break it down into two parts and differentiate each part separately. Step 1: Define the functionLet:Y=U+Vwhere U=(x+1x)xandV=x(1+1x) Step 2: Differentiate UTo differentiate U, we will ...
Answer to: Find the derivative of the following function. y = fifth root of (7x). By signing up, you'll get thousands of step-by-step solutions to...
Use logarithmic differentiation to find the derivative of the function. y'=,y=xx+7There are 4 steps to solve this one. Solution Share Step 1 We have given a function y=xx+7 We want to find out the derivative of the function y'. Explanation: We will use...
The derivative of a function can be calculated, performing some algebraic operations and in the case of the logarithmic function, applying the properties of logarithms. These are some of the properties: {eq}\displaystyle \log_ab=\frac{\ln\,b}{\ln\,a}\\ {/eq} ...
Finding Derivatives of a Function | Overview & Calculations from Chapter 20 / Lesson 1 115K Understand what derivative calculus is and how to find the derivative of a function. Learn the derivative rules, and practice taking derivatives by following examples. Related...