If f(x) + x²[f{x)]ª = 18 and f(1) = 2, find f'(1). %3D

Q: 4) f(x) e**+6x

A: If F(x) = f(g(x)) , then F'(x)= f'(g(x)).g'(x). dexdx=ex dxndx=n.xn-1. Quotient Rule of…

Q: Find the derivative of the function.…

A: The given function is hx=x2arctan8x

Q: find the n-th derivative of f(x). f(x)=e^-2x

A: Given function is fx=e-2x. Chain rule of differentiation states that: ddxfgx=f'gxg'x Now, we find…

Q: Find dy/dx by implicit differentiation.

A: To find: The derivative of x3y-xy3=4. Concept used: Chain rule of derivative: fgx'=f'gx·fgx Product…

Q: Compute the indicated derivative. d + 7x)(x2. dx x = 2

A:

Q: part ii, thank you very much.

A:

Q: FIND ANTI DERIVATIVE a) S 2. +9 dx x マ d x 1-4x6

A:

Q: Find the derivative

A: The first derivative of f(x) is represented byf'(x) and the second derivative is represented by…

Q: Find the indicated derivative. df If f(x) = x3, find dx 8 df dx |x = -11 || X 32 X = 10 X 1 2 11

A:

Q: Find the derivative of y with respect to x. 2. y²(x + 2y) = e²

A: Given,

Q: 1 y = V2x+5 /2х+5

A: By see this solution

Q: 10. S(2x – 3) dx e 2x2 - ебх

A:

Q: what is the second derivative of y(t)=e^-2t and y(t)=e^-3t

A:

Q: Find the derivative of y with respect to the independent variable. x2 y =log 8 Sx+1 1 8x+1 O In8 x2…

A:

Q: S-2(x-1 - x²) dx 5.

A:

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

A:

Q: Consider the derivative function h (x) = 5x³ + 3x² – 4x + 4. What is the general antiderivative of…

A:

Q: Find the derivative of the function. s(e) = VE-5E f '(x) =

A: The given function is: fx=x-5x3 The objective is to find the derivative of the function i.e., f'x.

Q: Find the derivative of f(x)=(x+4)e^(5x)

A: We have to find the derivative of f(x) ,where f(x) is given by

Q: 1. Find the first derivative of y: y=x-6x³+2x²

A: Topic = Derivative As per guidelines , At  a time only one question can be answered. please repost…

Q: find the first derivative of   F(x) = e(x+5)

A: Given,

Q: Find the derivative of the function y, below. y = 6x(ln a + In 5) – 8x + e ||

A: Given that y=6x(lnx+ln5)-8x+e To find the derivative of y

Q: y = e* - cos 3x + xlog.(1+x)

A: By using some formula of derivative

Q: Find the first derivative of the function * 4 f (x) = Væ + 4

A:

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

A:

Q: Find the second derivative of y = Vx² +x-3 O 6/x O 12/x^5 O 6/x^2 O 12/x^3

A: dxndx =n.xn-1 dcdx =0 ; where, 'c' is an constant number.

Q: f y=x^2(e^x)

A: Derivative: ddx(u.v)=u.dvdx+v.dudxy=x2(ex)Here u=x2,v=ex

Q: Find the derivative. x(x dx d [5x (x* + 1)°]-I dx

A: Given : d/dx[5x(x^4+1)^6]

Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

A:

Q: Find the derivative of f(x)=(x−2)e^(−3x).

A: The first derivative of the function f(x) = (x−2)e−3x is calculated as follows.

Q: Find the derivative of the function: f(x)=ln[x^2÷(x+1)^3

A: Formula:

Q: Find the derivative of f (a) = e" (x² + 2).

A:

Q: 10. Solve for the derivative of y IMPLICITLY 22 + Væ³ + 2y= y²

A: Note: According to our expert guidelines only first individual question is to be answered, kindly…

Q: Find the function with the derivative f'(x) 3x = e whose graph passes through the point P| 0,

A:

Q: Find the derivative of the function - 3x f(x) = 3 ln(x) + e - df dx

A:

Q: If f (x) = In (4a + 1), then its third derivative is f(3) (æ) = %3D

A: In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

Q: y = V5х+7

A:

Q: Find the derivative of the function. f(x) = ln x/(x2 + 1)

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Q: 1 Find the derivative of the function : ƒ(x ) = V |2x + 3

A: The given function is: f(x)=12x+3 Let, u=2x+3. So, f(u)=1u=u-12 and u=2x+3

Q: Compute the indicated derivative. d + x)(x5 – x)]. dx x = 1

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Q: Find the derivative of f(x)=

A: We use the quotient rule of logarithm to simplify the expression

Q: Find the derivative of the function y, below. y = 2x(ln x + In 7) – 2x + V2 dy da

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Q: 4) /() =2-2 3. 5) y = x*+2x+1 6.) f(x) =

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Q: Find the equation of the tangent line to the function f (x) = e*²-1 ln(x + 1) when x= 0.

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Q: Find the second derivative f"(x) for f(x) = e(#+2)*.

A: First calculate the first derivative for f(x) using the chain rule.…

Q: Find the derivative. f(x)=tanh(2 + e^3x)

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Q: Find the derivative of the function f(x) = 3 ln(x) + e5ª. df = dx

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Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

A:

Q: Find the derivative of the function f(x) below. f(x)=ln(5−e^(−4x)) f′(x)=

A: Explanation: Given that, f(x)=ln(5-e-4x) Differentiate both sides with respect to x.…

Q: Determine the value of the derivative function for Ax) = (x + x)(x- 2) at x = 2. %3D A 6 в О с 5 D1

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.