(c) Find an expression for the second derivative of 1/g(x) in terms of g, g', and g", explaining your calculation carefully.

Q: Find the first derivative of g(x) = - 5 In(x)cos(r"). g'(x) =

A:

Q: B) Using the definition of derivative, find -if y = dx 1-x

A:

Q: Find the derivative. g(x) = tanh-1(x?)

A:

Q: find the derivative of y with respect to the appropriatevariable. y = ln (x2 + 4) - x tan-1 ( x/2)

A: We use the chain rule and product rule

Q: What is the derivative of the function f(x) = e-2x?

A:

Q: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

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Q: - 3x Find the derivative of y with respect to x if y = e

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Q: find the derivative of y with respect to the appropriatevariable. y = tan-1√(x2 - 1) + csc-1 x, x…

A:

Q: Derive the formula for the derivative with respect to x of csc x.

A: We will write cscx= 1/sinx  Then we will use the quotient rule to differentiate

Q: Find the derivative. y = cos-1(x2)

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: tind the first derivative of the fanction i2 () =メ ニフ(x-1)

A:

Q: Find the derivative of the function g(x)= tanx/e^x.

A: This problem can be solved by the quotient rule in derivatives.

Q: Find the derivative of the function y = ln(9 – e-ª).

A:

Q: 2) Let y = xe* and find the first derivative y'. Where is y'>0?What does this tell you about the…

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Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: derivative

A:

Q: Q3:- Use the definition of derivative to find the tangent and normal equations of f(x) = x-3

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Q: Compute the derivative of the function y=x2/ln x at x=e.

A:

Q: how do you find the second derivative of f(x)=ln(x)?

A: on differentiation we get

Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

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Q: 8. Find the derivative of the function. y= In(1+x)

A:

Q: 2. Find the derivative of g(x) = 2x sin x.

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Q: Determine whether the following statement is true or false, and explain why. The derivative of ln kx…

A: if y = ln x Then y'=1x

Q: Find the derivative of the function y = ln(9 – e-"). f'(x) =

A: Given that y=ln(9-e-x) To find : Differentiation  y'=f'(x)=ddx(ln(9-e-x))=19-e-xddx(9-e-x)=e-x9-e-x

Q: 3) Find the first derivative of y=(In x)"

A: According to our guideline 3 subparts of question or the first question can be answered and rest of…

Q: Find the derivative of f(x) = -1 csc (cos r)

A:

Q: Find the second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: Determine the derivative of g ( x ) = 3 e-4 x*sin(7 x) with respect to x. = (x), 6

A: As per the guidelines, we need to author the 1st question.  We know that product rule is given by…

Q: 1+ cos x y = In 1-cos x

A: This question is based on chain rule differentiation.

Q: Find the derivative of  y=ln [tan-1(7x5)] with respect to x.

A:

Q: Find the derivative of the function. h(e)- (-1) ( 1) +]

A: Given ht=t4-15t3+16

Q: 2. Find the derivative of the function. y = e* In (sinæ)

A:

Q: Find the second derivative of the function f(x) = sin x2

A: Given f(x) = sin x2 To find d2f(x)dx2

Q: Find the derivative of the function y=cos(3 In x).

A: Given y=cos(3lnx)

Q: y = cof'/ x2-1 x²+

A:

Q: 4 Find the first derivative of y = In X +

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Q: Find the derivative of y with respect to x. y = In (tan -1 (9x5))

A: Given : y=lntan-19x5

Q: What is the derivative of the function  x^8(ln(x)), and what can I substitute for x to make the…

A: We have to find derivative dy/dx and point where dy/dx =0y is given below:

Q: 17) Find the derivative of y = x? COs x - 2

A:

Q: 3. Find the second derivative of f (x) = e²/*° and fully simplify your answer.

A: fx=e2x3

Q: 3. Find the second derivative using implicit differentiation x² + y? = 4

A: Given that x2+y2=4To find implicit differentiation

Q: 14. Find the derivative of the function using the definition of derivative. f (x) = V1 – x

A: Derivatives

Q: What is the first derivative of g(x) = ln #*+1? x2

A: Derivative of ln(x):       ddx(ln(x))=1x Division rule of derivative:-…

Q: Find the derivative of the function f(x)=(x²+e* + sin x)*.

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Q: is the derivative of In

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Q: find the derivative f(x) = sin (x^−3/e^-x )

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Q: c. Find the derivative of y =+- et x3 cOS X 2

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Q: -5

A:

Q: Find the first derivative of v with respect to x

A: Given,

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.