Let be a differentiable function such that f(3)=2.345 and f'(x)= ln(x^2+1).What is the value of f(5)?

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the 7th derivative of: f(x)=sin(x)cos(x) f’=? • • •

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Q: find derivative of g(x)=integration3x2x (u2-1)/(u2+1) du

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Q: On which derivative rule is integration by parts based?

A: Integration by parts is based on product rule of derivative. Mathematically, Product rule of…

Q: Determine the derivative of f(x) = Cosh(5 x) csc(x)

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Q: Find the derivative. Simplify where possible. hx) = (1 - cosh x) /( 1 + cosh x)

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Q: 3.

A: Indefinite Integration

Q: Find the derivative of sinh(x)tanh(x).

A: As per our guidelines I am solving only first problem please repost other question.  y = sinh(x).…

Q: Find the most general anti-derivative or indefinite integral and check the answer by differentiation…

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Q: ) y = In³ )) (tanh²(scc '(x²)

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Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: Compute for the derivative of the function using logarithmic differentiation g(y) =…

A: Logarithmic differentiation: - The use of logarithms to derive the derivatives of some difficult…

Q: Find the second derivative and the points of inflection using the second derivative f(x) = ln(x) /…

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Q: Find the anti-derivative: x2/3 dx. Upload Choose a File

A: Using simple integration method to solve the question.    Attached below is the detailed solution.

Q: y=9 arctan (x+sqrt(1+x^2) )

A: ddx(xn)=nxn-1 ddxx =12x ddxtan-1(x)=1x2+1 Chain Rule: if f=f(u) where u is a function of x then…

Q: Show that (x ln(x)) ‘ = 1 + ln(x) using the Product Rule for Differentiation.

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Q: What is the anti derivative of  f(x)= 2sin(x)-sec2(x)

A: Given information

Q: compute the derivative. f (x) = ln(ex − 4x)

A: We can use chain rule ( Nested function form ) of differentiation to find the derivative. According…

Q: Use logarithmic differentiation to find the derivative of the function. y = (sin 3x)In x sin()…

A: Formula used:If (x) and g(x) are two differentiable functions, then following rules  are efined as;

Q: Find the 139th derivative of y=cos x а. Cos x b. Sin x С. -Cos x d. -Sin x

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Q: What are the formulas for differentiation and integration? How are they applied?

A: To write: Formulas for differentiation and integration.

Q: Use the First Derivative Test to find the relative extrema of x – 3 f(x) ex

A: The given function is fx=x-3ex. We need to find the realtive extrema. Concept used:  Consider x=c is…

Q: Find the second derivative of g(x) = sinh(x) cosh(x)

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Q: implicit derivative to find dy/dx of    xy + arcsin(y)+2^y=ln(x)

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Q: The second derivative of y = ln(sec x) is а) у 1 - tan x b) y = tanx sec x c) y = secx · tan x d) y"…

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Q: Find the derivative. f(x) = x sinh(x) - 4 cosh(x) %3D f (x) =

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Q: Find 1st and 2nd derivative of:   f(x)=(5x^4 + 3x^2)*ln(x^2)

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Q: FInd the derivative of f(x) =ln 1+ex/1-ex

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Q: Find the derivative of y = arctan(x) by using implicit differentiation on x = tan(y).

A: Consider the provided function y=arctan(x).

Q: what is the derivative of f(x)=ln(tanhx)

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Q: Compute the derivative. Use logarithmic differentiation where appropriate. 10 1+ dx 10 1+ dx 10 In…

A: Answer: ddx1+10xx = ln1+10x-10x+10 1+10xx

Q: Find the derivative of the function y = x tanh−1 x + ln√(1 − x2)

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Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: nd derivative of f(x) = x In(x)

A: We have to find the second derivative of the given function

Q: Solve for the derivative of the Inverse Hyperbolic Differentiation. 1. y = sin h-1 (2x2 - 1) 2. y…

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Q: Use high-accuracy differentiation formula O(h) to estimate the first derivative of f(x)=log.x.…

A: Consider the given function, fx=logx Here we need to estimate the first derivative of the given…

Q: Find the derivative of  f (x) = ln( ln (ln 3x))

A: To find the derivative of f(x) = ln( ln (ln 3x)), differentiate f(x) with respect to x.

Q: is the derivative of In

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Q: Calculate the derivative of the function y=log2 x ln (2x) at x=1.

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Q: Find the derivative. y(x) = x tanh−1(x) + ln (sqrt (1-x^2))

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Q: Find the derivative. Simplify where possible. y  = x tanh-1 x   + In √ (1- x2)

A: We have given that, y=xtanh-1x+ln1-x2 We have to find the Derivative of this function i.e. y' As we…

Q: Compute the derivative of the given function. f (x) = 2 ln x – vT

A: Given fx=2lnx-x To find the derivative:

Q: Find the first derivative of the function below: f(x) = arctan(sec(x ))

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Q: What is the 2nd derivative of y=cosh(x+y)?

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Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: The second derivative of an anti-derivative of a differentiable function F R-R is: O possibly…

A: The second derivative of an anti-derivative of a differentiable function f:R→R is

Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.