To solve the derivative of In(sqrt x), the chain rule has to be used for this process. Learn the steps to solve the derivative of In(sqrt x) plus how to understand an application of this method in real life. Steps to Solve If we want to find the derivative of ln(√x), we will...
dxd(ln(x))=x1 =2ln(x)x1 Simplify2ln(x)x1:x2ln(x) =x2ln(x) Enter your problem Popular Examples Frequently Asked Questions (FAQ) What is the derivative of (ln(x)^2) ? The derivative of (ln(x)^2) is (2ln(x))/x ...
Derivative of arcsin x Derivative $f’$ of function $f(x)=\arcsin{x}$ is: \(\forall x \in ]–1, 1[ ,\quad f'(x) = \dfrac{1}{\sqrt{1-x^2}}\) Proof Remember that function $\arcsin$ is the inverse function of $\sin$ : \[\left(f^{-1} \circ f\right)=\left(\sin ...
Find the derivative of y=ln|cos(lnx)|. Using Chain Rule to Differentiate Complex FunctionsThe question presents a function that is a composition of three functions, two of which are the natural logarithm function and the third is a cosine function. Using the Chain Rule from Calculus we find...
Find the derivative of the given function Let's see how messy it gets... ##\dfrac{dy}{dx}=\dfrac{(1-10x)(\sqrt{x^2+2})5x^4 -(x^5)(-10)(\sqrt{x^2+2})-x^5(1-10x)\frac{1}{2}(x^2+2)^{-\frac{1}{2}}2x}{[(1-10x)(\sqrt{x^2+2})]^2}##... ...
•csc(x)—cosecant •arcsec(x)—arcsecant •arccsc(x)—arccosecant •arsech(x)—inverse hyperbolic secant •arcsch(x)—inverse hyperbolic cosecant •|x|,abs(x)—absolute value •sqrt(x),root(x)—square root •exp(x)—e to the power of x ...
Find the derivative ofy=sec(x). Question: Find the derivative ofy=sec(x). Identities and Trigonometric Derivatives: To differentiate a trigonometric function, it is sometimes necessary to redefine it before applying the differentiation theorems. ...
If f(x)=prod(n=1)^(100)(x-n)^(n(101-n)); then (f(101))/(f'(101))= 05:27 Find the derivative of y=(sinx)(e^(sqrt(sinx)))(lnx)(x^x) 04:55 Find the derivative of y=(x^(lnx))(secx)^(3x) 04:43 Find the derivative of y=((lnx)^x)/(2^(3x+1)) 04:08 If...
Step 1. Find the derivative of f(x) utilizing the chain rule. {eq}\begin {align} \displaystyle f(g(x))\displaystyle & = \tanh (\sqrt...Become a member and unlock all Study Answers Start today. Try it now Create an account Ask a question Our experts can answer your tough ...
Furthermore, it also holds when c is fractional. This allows us to calculate the derivative of, for example, the square root: d/dx sqrt(x) = d/dx x1/2= 1/2 x-1/2= 1/2sqrt(x) Exponentials and Logarithms The exponential function exhas the property that its derivative is equal to...