24. 100 e Find the derivative of y with respect to 0 if y In 100 1e dy de

Q: If a is a positive integer, then the slope of the tangent to the graph of y = a²x – a ln(ax +1) at z…

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Q: Find the value of the derivative y′(x) at x=0 for the function given by ey+xy=e.

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Q: A) find the derivatives for the following: 1) y = In(In(sin¯'(e?r))) – 5-Inx 2) Y=sech-1(log, 93*) +…

A: Chain rule for differentiation: Let y=fghx then dydx=ddxfghx=dfghxdghx×dghxdhx×dhxdx Equation of…

Q: 4.62. Evaluate the derivative of the Gamma function and see dT'(x) r'(x) = dx ' (In t)e"'dt

A: To differentiate the gamma function:         Γ(x) = ∫0∞tx-1e-tdt Integral definition of gamma…

Q: 3. Find the value(s) of k for which y = e satisfies the equation y+2y' = y" derivative) (note: y" is…

A: k = 1+2, 1-2explanation is given in below step

Q: Which of the following means "first derivative" * O f(x) O y' O dy/dx all of the above

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Q: 1) Find the second derivative of y = csc 2 e cot 2e %3D

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Q: Find the Derivative of the given function. If y = e cos(54) then dy dt

A: Solution is given below:

Q: Evaluate the second derivative of e22.1.png acos(b/x) f(x) x2 if a = 323 and b = 0.5 at x = 3 using…

A: Given function is f(x)=323cos0.5xx2 Step value is ∆x=0.1

Q: D-the derivative is y = In Othe O is the (VW) 1 + Vē 1 0(√) 1 (1+√ē) O it O is 1 20(1+√ē) 1 0(1+√0)

A: Differentiation

Q: Find the derivative of the following function. y = In (x° +6)" dy %3D dx (Type an exact answer,…

A: Given: y=ln(x3+6)π To find the dydx=?

Q: Q3) Find the derivative of y for all functions the following (1) y = 0 (sin (In 0) + cos (In 0)),…

A: Since you have posted multiple questions, we have solved the first question for you, if any specific…

Q: Find the derivative of the following functions without skipping steps w = 7x sin (z?) – z? sin (y) +…

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Q: d mula sinh (t) = In (t + VE? + 1) and- (In(t)) = } %3D ne derivative of sinh(t).

A: Here we use rule of differenciation to find the required derivative.

Q: Q5:The derivative of: y(Y)= log,(sin (Y )cos (Y ))- log,(2*e

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Q: 10. Find the slope of the tangent line for the following function at indicated point: 1 f(t) at t =…

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Q: dy Find the derivative of the function In 3y= y sin 3x + etz Answer.

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Q: Let e - v = 1. Find each derivative. du dv (a) dv (b) du (c) Based on your answers to parts (a) and…

A: eu2-v-v=1

Q: Calculate the first numerical derivative of the following equation with the values xo = 1 and y o =…

A: Given function is fx,y=ex3y−sinx,  x0=1 and y0=15.6 for Δx=Δy=0.1 We have to find the first…

Q: Find derivative /differential of each of the following functions by using the appropriate formula.…

A: y=x2 e2x  dy / dx  =?

Q: Find the derivative of y with respect to x. y = sin (e 5t) e 5t e OA. 1- e 10t 5e 5t O B. 1- e 10t 5…

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Q: d'y of y = 5 cos T dr

A: The given function is y=5cosx. Obtain the first derivative of y=5cosx: dydx=5dcosxdx=-5sinx Obtain…

Q: Q2 find the derivative of the following: 1) y = 2sin?(5x) ,2) y = lnx'ncosh 5x ,3) xsin-14y = y…

A: See the attachment

Q: /4 Find the derivative of y with respect to t. (a) y = In(3te-1) (b) y = esin t (In t² + 1) (c) y =…

A: Given functions,  (a)  y=ln3te-1 (b)  y=esintlnt2+1 (c)  y=tlog3e(sint)(ln3) The objective is to…

Q: 大 If x < 0, which of the following has the derivative 1 dy (1 – a)Va - 2a =? dx |3|

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Q: Q5:The derivative of: y(Y)= log,(sin( )cos (Y ))- log,(2*e* )? sinų sin y In 7 cosy In 7 cosy cosy…

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Q: The derivative of y=eov? +cosh/x equals Select one: O y' = 2/x et +sinhx + sinh/x O None O y'=@ov +…

A: This is a composite function. Therefore we have to use rules for derivative of composite functions.

Q: 6. y = In (e* + e") 7. y = tan e + etanax 8. y = In(x + Vř +1) 9 y = Arctan(;

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Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: Take the derivative of the following: Dy= 3xe y = e (3) e y = @y= In () 10 Y=ln (In x)

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Q: 9. What is the derivative of cos(at5 + b) with respect to t?

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Q: Can i get help step by step?

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Q: 7. Find dy and hence determine the rate of change of y with respect to x for the following…

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Q: 8. What is the derivative of y= Vu in terms of x? dy a) 2/y dulas b) 2vu d) 2/u

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Q: Find the derivative of y with respect to t at t=2 if a) y = cos (x) – cos(1+x²) and x = [sin(t – 2)…

A: The derivative of y with respect to t is:

Q: can you help me step by step with this problem?

A: Find the derivative with respect to s.

Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

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Q: The third order derivative of the function y = In(1 – x) - at x = 0 is et O A. Undefined OB. C. 4 D.…

A: As per our guideline we supposed to answer only first question , kindly re post other as next…

Q: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

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Q: Can i get help step by step?

A: We take ln on both sides and use logarithmic differentiation. Using the product rule and power rule…

Q: Find the derivative of the function. sin(x) y = In(1 + 7v) dv g'(x) = Jcos(x)

A: Solution

Q: Find the antiderivative of the given derivative. ds 14(4? – 1)3 dt S =

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Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: - 18x Find the derivative of y with respect to x if y = e dy %3D dx

A: We have to find the derivative

Q: Find the derivative of y with respect to x: ,2 2 X'e y = log,2 x+2) Evaluate the integral: -1 cos…

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Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: 3. Evaluate the following derivatives: a) y = In[sinh(2x)] b) f(t) = tanh-1 VE

A: Derivative of the inverse hyperbolic function formula: -  ddx(sinhx)=coshx ddxtanh1x=12ln1+x1-x…

Q: Find the derivative of y with respect to the independent variable. 20) y = 7cos TO A) -17COS TO In 7…

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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.