Find the first derivative of the function. {eq}\displaystyle y = \sqrt {(3 x + 13)^2} + 17 x^{\displaystyle -2} {/eq} Chain Rule and Power Rule: The derivative of power form function {eq}x^n {/eq} where n can b
Find the first derivative of the function. {eq}f(x) = (\cos(3x^3))^2 {/eq} Chain Rule: Nested functions are differentiated using the following rule: {eq}\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}v(u(x)) = v'(u(x))u'(x) {/eq} This rule is known as th...
The derivative of a functionfis an expression that tells you what the slope offis at any point in the domain off.The derivative offis a function itself. In this article, we will focus on the functions of one variable, which we will callx. However, when there are more variables, it wor...
How to Find the Derivative of a Function Using the Limit of a Difference Quotient: Example 1 Find the first derivative of f(x)=2x−3. Step 1: Identify our function. The function that we are finding the first derivative of is f(x)=2x−3. Step 2: Find...
Find the derivative of the function )1()3(2+-+=x x x y 相关知识点: 试题来源: 解析 y' = 3x² + 2 原函数整理后为 y = x³ + 2x - 1 求导过程: 1. 对x³项应用幂法则,导数为3x² 2. 对2x项应用线性法则,导数为2 3. 常数项-1导数为0 组合之后导数为 y' = 3x² +...
Find the derivative o fthe function Find the derivative o fthe function 相关知识点: 试题来源: 解析 Combinin gth ePowe rRule ,Chai nRule ,an dQuotien tRule ,w eget Combinin gth ePowe rRule ,Chai nRule ,an dQuotien tRule ,w eget \$g ^ { \prime } ( t ) = 9 \left( \frac ...
Given function is: {eq}f \left(x \right) = 3x^2 + 5e^x {/eq} To find the first derivative of the function {eq}f \left(x \right) {/eq}: $$\begin{a... Learn more about this topic: Finding Derivatives of a Function | Overview & Calculations ...
Applying the Rules of Differentiation:To find the speed at which the value of a function is changing at a given point, we need to differentiate the function. The first derivative of a function represents the slope of the function. Differentiation of a position function of a particle with...
Find the first derivative and simplify them a) {eq}f(x) = sin \pi^2 + 5 \pi {/eq} b) {eq}f(x) = x \tan x {/eq} c) {eq}f(x) = \frac{x + 1}{x - 1} {/eq} d) {eq}f(x) = - \sec^3 x. {/eq} Deriva...
【题目】Find the derivative of the function.$$ g ( x ) = \frac { \arcsin 3 x } { x } $$ 相关知识点: 试题来源: 解析 【解析】 $$ \frac { 3 x - \sqrt { 1 - 9 x ^ { 2 } } \arcsin 3 x } { x ^ { 2 } \sqrt { 1 - 9 x ^ { 2 } } } $$ 反馈 收藏 ...