y=ln(2x)=ln(2)+ln(x) Step 2: Differentiate the functionNow we differentiate both sides with respect to x:dydx=ddx(ln(2))+ddx(ln(x))Since ln(2) is a constant, its derivative is 0. The derivative of ln(x) is 1x:dydx=0+1x=1x Step 3: Write the final answerThus, the ...
Find the derivative of the function: {eq}f(x)=\ln\left[\left(\dfrac{2x}{x+3}\right)\right] {/eq}Derivative of the Function:Derivative of the function means we have to calculate the change in the rate of the function. If the function is a complex logarithmic function, then...
Find the first derivative of the following function: f(x) = (x^3 - 2x) (x^{-4}+x^{-2}). Find the first derivative of the following function: f(x) = a^(-bx) Find first and second derivative of the following: y=x \: ln(x). Find first and second derivative of the follo...
The slope of aconstantvalue (like 3) is always 0 The slope of alinelike 2x is 2, or 3x is 3 etc and so on. Here are useful rules to help you work out the derivatives of many functions (withexamples below). Note: the little mark’meansderivative of, and f and g are functions. ...
derivative of(2x+3)3(x2+3x) Solution Hide Steps Solution steps Popular Examples Frequently Asked Questions (FAQ) What is the derivative of ((x^2+3x))/((2x+3)^3) ? The derivative of ((x^2+3x))/((2x+3)^3) is (-2x^2-6x+9)/((2x+3)^4) ...
Question 1 y = e^(x^3) * ln x^2 dy/dx = {d[e^(x^3)] / dx}(ln x^2) + {d(ln x^2) / dx}[e^(x^3)] = 3x^2[e^(x^3)](ln x^2) + (2x / x^2)[e^(x^3)] = [e^(x^3)][3x^2(ln x^2) + (2 / x)] Question 2 should be f(x) = (1...
Find the derivative of y=tan^-1 (ln 2x) with respect to x. Find the derivative of y = In (tan^{-1} (7x^5)) with respect to x. What is the derivative of arctan(x) + 4e^x? What is the derivative of \ln(x-1)? What is the derivative of y = \sin^3(x) + \sin(x^...
Find y' if y= ln( x^2 + y^2) I thought this was just a regular natural log derivative combined with the chain rule. So what I got was (2x + 2y)/ (x^2 +...
a) f(x) = (6 x ^2 -x) ln (x) b) g(x) = ln(x - 5.1 x ^{-1}) c) s(x) = ln ((x - 9)^2) Find the derivative of the following functions: \\ y = 4x^3 (2x - 5) Find the derivative of the following functions. 1. \ln((...
{ln^{3}(x)} - \frac{5xe^{\frac{x^{3}}{ln(x)}}}{ln^{2}(x)} + \frac{x^{4}e^{\frac{x^{3}}{ln(x)}}}{ln^{4}(x)} + \frac{2xe^{\frac{x^{3}}{ln(x)}}}{ln^{3}(x)}\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac...