Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: Arctan(x) ln(x^3 + 2) find the derivative    F(x) = arccos(3x^2) find the derivative

A:

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

Q: Find an equation of the tangent line to the graph of the function at the given point, (a) use a…

A: So the slope of the tangent is 4

Q: 2. Implicit Differentiation Explain when you have touse implicit differentiation to find a…

A: Consider the following example xy=1

Q: Differential function of x2 + 2x + 3tanx

A: The given function is: x2+2x+3 tan x

Q: Using Leibnitz theorem, the nth derivative of xy, is

A: We have to find nth derivative of xy1 using Leibnitz theorem.

Q: Find the derivative of the function 2 tan- (). y (Use symbolic notation and fractions where needed.)…

A:

Q: 3x y=3- + Arccos V8-x3

A: We have to find out the first derivative  .

Q: 6. Determine the 19th derivative of the function y=sin(x). Fully explain the process you used to…

A:

Q: True Or False: Derivative of (arcsin(x^3))^4 = [12x^2 (arcsin(x^3))^3] / sqrt(1-x^6)   Show…

A:

Q: Find the equation of the line tangent to the graph of y = 4 ln(x) at a = 2. Enter exact values.…

A: detailed solution is given below

Q: e first derivative for the +1)(x +2) 2)

A: Find the first derivative. y=(x+1)(x+2)(x-1)(x-2)

Q: Find the Indefinite Integral and Check the result by differentiation

A:

Q: What is the derivative of 2(x)ln(x)+x

A:

Q: central-difference method to approximate the derivative of f(x) = ln x² with value Use of x at 1.8,…

A: As multiple questions are there and it is not mentioned that which question to be solved, I will…

Q: 1950, a seed was planted same as the year as Jilian was born. When she celebrated her debut, the…

A: Given Information - Height of the tree when Jilian was of 1 year = 5m Height of the tree when Jilian…

Q: Can you help me with this problem step by step?

A: The equation is given by

Q: 5th derivative of y = log x^5 to the base 2

A:

Q: Compute the derivative of the function y = 6 sin-'(x) at the point x = (Use symbolic notation and…

A:

Q: 3 + 2x +5

A: GIVENy=x3+2x+5   and x=2

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A:

Q: This is determined by the largest derivative, or the highest level of differentiation, present in a…

A: The highest level of differentiation present in a differential equation is known as "order" of the…

Q: Find Derivative Using Implicit Differentiation: 11. Find derivative Use Leibniz notation in your…

A:

Q: Find the derivative of y with respect to x Y=5 ln (3 ln x)

A: Given, y=5 ln (3 ln x) We have to find derivative of y with respect to x.

Q: Find an equation of the tangent line to the graph of the function at the given point, (a) use a…

A: Equation of tangent line in slope and point (x1, y1) form is given by

Q: Compute the derivative. y = cos (te-61) (Express numbers in exact form. Use symbolic notation and…

A: y = cos(te-6t) here we use chain rule and derivate the equation  with respect to t

Q: d 14.- - (logx) dx

A:

Q: Find the derivative of the function. f(x) = ln(2 − x2)   Thank you for your help!

A: Given function f(x) = ln(2-x2). Here we need to find the derivative of f(x) with respect to x.We use…

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: See the details solution in below

Q: find the derivative of sin(x)/2+cos(x) express numbers in exact form. Use symbolic notation and…

A:

Q: Derivative of ln[cosx/4-3x^2]

A:

Q: Find the derivative of the function. y = square root of 1 - x2 − x cos−1(x)

A:

Q: Use logarithmic differentiation to find the derivative of the function. y = (ln(x))cos(5x) y' =

A:

Q: Find an equation of the tangent line to the graph of the function at the given point, (a) use a…

A: It is given that equation of the graph is y=x3 ln x4 and  a point P-1, 0. (a) Find the slope of the…

Q: Estimate the slope of the tangent line at the point x=12, for f(x)=ln⁡(x). (Use decimal notation.…

A: Given:- f(x) = ln(x) and point x = 12.

Q: Find the second derivative of the f(x)=9+8x ln x function

A:

Q: Derivative of arctan(ln(n))

A:

Q: Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),      (3,…

A: To Find an equation of the tangent line to the curve at the given point. y = ln(x2 − 3x + 1),…

Q: Find the derivative of these functions with respect to x.   xsin-1(In(x))

A:

Q: Find the derivative of the function. y = arctan(root1-x/1+x)

A: y=arctan1-x1+x

Q: The L'Hopital rule and The derivative of the exponential function. lim (ex + x³)*:

A: Use l hospital rule

Q: 7- cosh(x) 7+ cosh(x) Use appropriate rules of differentiation to find the derivative of Gx) =-

A:

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: Given query is to give an example of exponential and logarithmic differentiation.

Q: sinh x – cosh x + ecothx dx - sinh2x

A: Let's find.

Q: Find the derivative of y sinh-(13x). (Use symbolic notation and fractions where needed.)

A:

Q: find the equation of the tangent line to the graph of the function y = ln(x^2) at the point (3, 1).

A:

Q: sinh (2.Inx) n(coshx+Sinhx)+in(cashx-sinh x).

A: We have to rewrite the given expression by using the exponents.

Q: First Derivative of: (tan3(2x)) / x1/5 + ln(7x+4)

A: (U/V)' = (VU' - UV')/V^2

Q: 3 sin(x) +x² In(x) – 2x Find the derivative of f(x) = using derivative rules.

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: