Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x) = etan2x

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 derivative of the given function. Infsech(x) + tanh(x)) 1) sechx+tanhr sinhx+1 sechx-tanhx…

A:

Q: Compute the derivative using derivative rules that have been introduced so far. y = (x 4 + 5)3

A: Given equation is y=x4+53 Applying derivative with respect to x: dydx=dx4+53dx Using the power rule…

Q: Find the derivative using the long method y = vx + 2

A:

Q: (x²+1)* V1-x y = In

A: Use the chan rule of derivative then simplify the result.

Q: The instantaneous velocity of a particle is defined as the derivative of some functions. Select one:…

A:

Q: Find the derivative of ¤(x) at x = /3/2 where rsin-'(x) $(x) = eº tan 0 do. x2

A:

Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

Q: Find the derivative of the function using 3-step rule: v (t) = -.

A:

Q: Find the derivative of the function y = arctan x + x 1+x²

A: Given: y=arctanx+x1+x2Recall the formulas:ddxarctanx=11+x2     ..........1ddxuv=vdudx-udvdxv2…

Q: Find the derivative of the function f(x) = tanh(4x2 + 3x)

A:

Q: Determine the derivative of the function y=arcsin 2x / 1+x2 at x=2.

A:

Q: y = (Arccos 3x³)³

A:

Q: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

Q: S(x)= Jx-5

A: given that f(x)=1x-5 find the derivative from first principle f'x=limh→0 fx+h-fxh

Q: Calculate the derivative of the function y=1+cosxsinx.

A: Given: y=1+cosxsinx we know that for finding derivative of given function we need to use product…

Q: Compute the derivative using derivative rules that have been introduced so far y = cos4 θ

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: Find the derivative of: y? – 4x = 0 at point (4,4)

A:

Q: Determine the derivative of y=(x−1)4 without using the power rule.

A:

Q: Find an equation of the tangent to the curve x+ Vy = 3 at point (4, 1). [Hint: Use implicit…

A:

Q: Find the derivative of the function

A: Given:y=arctanx+x1+x2Differentiate formula:ddxarc tanx=11+x2ddxuv=vdudx-udvdxv2

Q: Find the derivative of the function y = 2x arccos x − 2√(1 − x2 )

A: If the two functions f(x) and g(x) are differentiable (the derivative exist) then the product is…

Q: Estimate the derivative of f(x) = sinx atx = ~-

A: Consider the provided function, fx=sinx at x=π2 Find the derivative of the function. First, we…

Q: Compute the derivative using derivative rules that have been introduced so far y = ex-12

A: To differentiate y=ex-12, with respect to x, apply the exponential rule of differentiation,…

Q: Find the derivative of the function f(x) = cosh(8x + 1)

A:

Q: 1 y = ┤㈑┤慈┤

A:

Q: Shows the derivative function of: TC = Q³ + 2Q²  + FC(Q), where TC = Total Cost and FC = Fixed…

A:

Q: Find the derivative of the function. y = tanh6(9x) %3D y' =

A:

Q: Estimate the derivative of f(x) = sinx at x = π/6

A: Since,it is known that the derivative of the function with any variable measures the rate of change…

Q: Find the derivative of the function y= arctan x +x/1+x2

A:

Q: calculate the derivative y = ecosh−1 x

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…

Q: Find the derivative of the function y = arctan x+ 1+x?

A: To find: The derivative of the function . Calculation: Find the derivative of the function.

Q: Find the derivative of xn by first principle or ab-initio method.

A:

Q: What is the approximate derivative of f(x) = x2e* , using backward-difference approach at %3D x-2…

A: The main objective is to calculate the value of the derivative of the function f(x)=x2ex at the…

Q: Find the Derivative of the hyperbolic function (3.11): y=sech(x)*(1+ln(sech x))

A:

Q: Find the derivative of the function. y = arctan 1 + x 1 - X y' =

A:

Q: Find the derivative of: x²y = (y + 2) + ry sin(x)

A:

Q: Find the derivative of y with respect to the appropriate variable. y = cosh12 x+ 5

A:

Q: Find the derivative of y = 21+arctan x

A: By using derivative formula

Q: Determine the derivative of y. y = eV14x+6 %3D

A: Please refer the attached image for complete solution.

Q: Solve for the derivative of the function using chain rule. 14. f(x)= 3lnx 15. f(x)= cos(cosx))

A:

Q: 4) Find the derivative of y = arctan(x² + 3)

A:

Q: Determine the second derivative of f(x) = x²e²x at x = -2 with a step-size of h=0.50 using Central…

A:

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: Find the values of x in the interval [0,2π] where the tangent line to the graph of y= sinxcosx is…

A: Given:y=sinxcosx,     [0,2π]

Q: 2.) y = tan¬1 – 6•x³ y' =

A: We have to find the derivative of the function: y=tan-1-6·x3 We know the formula of derivatives,…

Q: find the derivative of the fuction f(x)= 5sinx/3x+cosx

A:

Q: y=

A:

Q: Find the derivative of the function. Simplify wherepossible  x lnarctan x

A: Let f(x)=xlnarctanxDerivative formula:ddxlnx=1xddxtan-1x=11+x2arctanx=tan-1x