Use the definition of the derivative f'(x) = ļim ollowing functions. Show your step by step solution. h-0 to find the derivative of the OHI NC

Q: Find the derivative of f(x) = arccos 3x + arcsin 3x.

A: derivative of arccos(x)=-11-x2 and derivative of arcsin(x)=11-x2

Q: Find the derivative of f (x) = arccos 3x +arcsin 3x.

A: Given: f(x)= arccos 3x+arcsin 3x To find: Derivative of f(x)=df/dx=??

Q: Find the derivative using the appropriate rule or combination of rules. y = tan(x2 + 4x)

A: Consider the given function y = tan(x2 + 4x)

Q: In + arctan.

A: Given        y=1212In x+1x-1+arc tan x-1

Q: h(x) = Vx cos x

A:

Q: find the derivative using the appropriate rule or combination of rules.

A: Consider the given function

Q: find the derivative using the appropriate rule or combination of rules. y = (cos3 x + 3 cos x + 7)9

A: We have differentiation of nested functions . In nested function form of differentiation we have one…

Q: Calculate the derivative with respect to x of the other variable appearing in the equation. sin(x +…

A: The given equation is  sin(x+y)=x+cosy ...................................(1)  differntiate with…

Q: Find the derivative. Simplify where possible. g(x) =  e cosh 3x

A:

Q: find the derivative using the appropriate rule or combination of rules. y = (x3 + cos x)−4

A: Given that, y=(x3+cosx)-4

Q: Use the definition of the derivative to find the value of f'(2) if f(x)=x'-2x. Then use it to write…

A:

Q: Find the derivative and simply. 1+cosx (a) f(x) = 1-cosx (b) f(x) = 3x5 cot-1 x

A: Part aGiven,          fx=1+cosx1-cosx

Q: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

A: Use the Chain Rule combined with other differentiation rules to find the derivative of the following…

Q: Find the derivative of f(x) with respect to x ( f(x) = cos(x), find the f(x) by using the…

A: Given;  f(x)=cosx.

Q: Find the derivative of g(x)=sec(1/2x) tan (1/2x), simplify and using trignometry elimate tangent…

A: To find: the derivative of the below function.

Q: Find the derivative using the appropriate rule or combination of rules. y = tan3 x + tan(x3)

A:

Q: find the derivative using the appropriate rule or combination of rules. y = tan3 x + tan(x3)

A: A function is a relation between an input variable and an output variable wherein each input…

Q: y = tan(x² + 4x)

A:

Q: Find the derivative with respect to the independent variable. f(x) = tan (14x) f'(x) =O

A:

Q: Find the derivative. Simplify where possible. f(x) =ln  ( cosh x )

A: fx=lncoshx

Q: ■ Find the derivative of the function. Simplify wherepossible.  y = arctan sqrt ( (1-x)/(1+x))

A: Given function is y=arctan1-x1+x We know that ddxarctanx=11+x2 Therefore, dydx=11+1-x1+x2ddx1-x1+x

Q: Find the derivative of the function.

A: fx=arc sinx + arc cosx

Q: Compute the derivative using derivative rules. y = cot7 (x 5)

A:

Q: Use implicit differentiation to find the derivative of arctan(x).

A:

Q: Obtain the derivative formulas for csch x, sech x, and coth x from the derivative formulas for sinh…

A: Given functions are sinhx,coshx,tanhx.

Q: Find the derivative and simply. (a) f(x) = 1+cosx 1-cosx

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: find the derivative using the appropriate rule or combination of rules. y = sin(x2 + 4x)

A: Given y=sinx2+4x

Q: Find the derivative of the function f(x) = arcsin x + arccos x

A:

Q: Find the derivative. Simplify where possible. g(x)  =Cos h(In x)

A: The function is g(x)=cosh (ln x). We have ddxcoshx=sinhx. To find the derivative, apply the chain…

Q: Find the derivative using the appropriate rule or combination of rules. y = (x3 + cos x)−4

A:

Q: Find the derivative. Simplify where possible. h(x)  =In(Cosh  x)

A: Given: h(x)=lncosh x To find: we have to find the derivative of h(x)

Q: Find the derivative of the following functions using the long method (limits) y= tan x

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use the derivative implicitly to find the slope of the tangent line at the point ,0), Suppose y is a…

A: Given- siny+cosx=12 To Find- The slope of the above expression at the given point π3,0.

Q: f(x) = sin° (tan(5e2*))

A: We can find the derivative as below using chain rule.

Q: Find the derivative of the function. Simplify where possible. y   =arctan(cos θ)

A: Given:y=arc tancosθFormula:ddxtan-1u=11+u2.dudx

Q: Use the limit definition of the derivative and the addition law for the cosine function to prove…

A:

Q: Find the derivative of the trigonometric function f(x)=sin2x using the limit definition.

A:

Q: Find the derivative and simply. 1+cosx (a) f(x) = 1-cosx

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: Find the derivative with respect to 0: y = In(sece + tan 0)

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Q: Find the derivative. Simplify where possible. |(a) y = ln(coshx)

A: Find the derivatives

Q: Use the limit definition to find the derivative of the function f(x) = 6x – x2. Then find all…

A: NOTE: Refresh your page if you can't see any equations. . Limit Definition of the Derivative is

Q: Find the derivative of the following functions using the long method (limits)

A: Given: x= 12 t4-5t-3 To Find: limh→0xt+h-xth

Q: Find the derivative of the following function using the LONG METHOD (limits). Provide your…

A:

Q: Find the fifth derivative using product rule y = sin3xcos4x Where r is the last digit of your…

A: The fifth derivative of the given function can be found by differentiating the given function five…

Q: 2. f(x) sinx-1 %3D cosx

A: 2-Given- fx=sinx-1cosx To Find- The derivative of the above expression. Identity Used- Using the…

Q: Find the derivative using the appropriate rule or combination of rules. y = (cos 6x + sin x2)1/2

A:

Q: If f(x)=4x(sinx+cosx), find f'(x) f'(x)= Evaluate the derivative at x=2. Enter an approximation,…

A:

Q: By interpreting the function as a derivative, find the limit as x goes to pi over two when (sinx -…

A: From the definition of the derivative at x=a. f'a=limx→afx-fax-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.