what is the derivative of {eq}y=(2x+5)^4(4x+1)^{-2} {/eq} Differentiation: Consider a function {eq}\displaystyle y=f(x) {/eq} then differentiation is given by{eq}\displaystyle \frac{dy}{dx}=f'(x) {/eq} Derivative of {eq}\displaystyle [f(x)]^n {/eq} is {eq}\...
Differentiate: y = cos x / (sin x + 1). What is the derivative of f(x) times g(x), if f(x) = sin(x) and g(x) = x^2? Find the derivative of \sin x, \tan x, \cos x, \ln x, and e^x? Finding the first derivative. g(x) = \frac{1 + \sin x}{x + \cos x...
What is the derivative of y=ln((1x+15)21(1x−13)15(17x−7)5(9x+9)5) with respect to x ? dydx=There are 2 steps to solve this one. Solution Share Step 1 Given y=ln((x+15)21(x−13)15(17x−7)5(9x+9)5) Expanding the logarithm ln((x+15)21(x...
The derivative of the logistic sigmoid function, σ(x)=11+e−x,σ(x)=11+e−x, is defined as ddx=e−x(1+e−x)2.ddx=e−x(1+e−x)2. Let me walk through the derivation step by step below.ddxσ(x)=ddx11+e−x=ddx(1+e−x)−1[apply chain rule]=−(1+e−...
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^...
What is the first derivative ofg(x)=ln(4x^2+3x+2)Select the correct answer below:O ln(8x+3)O(4x^2+3x+2)/(8x+3) 8z+3○(8z+3)/(4z^2+3z+2) O 1/(4x^2+3x+2)(8x+3)/(m(4x^2+3x+2))O I 相关知识点: 试题来源: 解析 (dq(x))/(dx)=d/(dt)(ln(4x^2+3x+2)...
What is the derivative of tan^(-1)((sqrtx-x)/(1+x^(3//2))) at x = 1? 02:00 xsqrt(1+y)+ysqrt(1+x)=0 then (dy)/(dx)= 06:35 If y=f(x),p=(dy)/(dx) and q=(d^(2)y)/(dx^(2)), then what is (d^(2)x)/(... 01:34 If x=sin t-t cos t and y =...
We know the derivative of a function at a point(a,f(a))(or a number a,or x=a). Please consider the example below by using the Graphing-Calculator(TI-84plus).Example 1:Find the derivative of f(x)=x2-8x+10at the number 2,2.5,and 5 by using the Graphing-Calculator. Solution:...
Hint:To solve this question, we should know about the derivatives and the derivation formulas.This is because we can calculate the second derivative by the solving of the first derivative’s derivation again. The second derivative of any function is always the same if we calculate that by ...
Hence, the derivative of cosec x is"-cot x cosec x". Suggest Corrections 37 Similar questions Q. what is the derivative of |x|? Q. What is derivative of [1x]x Q. What is the derivative of loge x? Q. What is the derivative of |x−1| at x=2? Q. what is the derivative...