y = sin(In 2x) a. sinx b. In 2x c. cos(ln 2x) cos(In 2x) d.

Q: a. Use implicit differentiation to find the derivative dx b. Find the slope of the curve at the…

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Q: B. Find the first derivative for the following function. Do not simplify . 1+ cot(x) (a) f(x) = (2x³…

A: The following function are f(x) = (2x3 + 4)(x4 - 3x) f(x) = [1+ cotx] /cosx

Q: 3. Find the derivative of the following functions using the definition of the sine and cosine…

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Q: The second derivative of the given function is - 5 sin (2- 5x) -125 sin (2 - 5x) 125 sin (2 - 5x) O…

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Q: Find the derivative of the function below. (Do not simplify your answers, and SHOW ALL STEPS) f(x) =…

A: Use the concept of derivative of the form f(x) = uv

Q: 3. Find the derivative of the following functions using the definition of the sine and cosine…

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Q: 5. Find the following derivatives. Simplify and factor if possible. 1+ sin x (a) f(x) = ln(x* sin?…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the derivative of the following functions using the definition of the sine and cosine function.…

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Q: 2. Find the derivative of the following functions: 5x + 6 (a) y = 8х — 1 )(",-) 2 8. - 8 (b) r =…

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Q: 6. In(x³y²) = x² +y³

A: Let's find second derivative of given function.

Q: (b) Find the first 4 derivatives of f (x) =b cos (x), and use the results to find the following…

A: We find the first 4 derivatives.

Q: 13x Find the derivative of the function y = 2 tan¬1 (5x ). (Use symbolic notation and fractions…

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Q: Find d of the function given implicitly and evaluate the derivative at the given point. y = sin (…

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Q: 1. Find the derivative of the following trigonometric functions a) y = x sin(x) + cos(x) b) y =…

A: Given the trigonometric function

Q: 2. Find the derivative of the following functions: 4 -2 (a). f(x) = x* + 3x + 2e* (b). ƒ(x) = 2…

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Q: Find the derivatives of the following functions using the rules of differentiation. Simplify your…

A: Given that        y = 2x/(3x+1) Here we have to find the derivative of the given function by using…

Q: C. Find the derivative of each of the following functions using Differentiations Rule/Chain Rule. 1.…

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Q: e the chain rule to find and simplify the derivative of the function g(x) = cos(sin1(3x)).

A: Solution:- Differentiate with respect to x with the help of chain rule.

Q: 3. Z(t) = 4 log3 (t) – In(t) Z'(t) =

A: Given: To find: The value of z'(t).

Q: Q. Find the second order derivatives of the following functions f (x). 3x-x i) Tan 1-3x

A: Derivative of function

Q: 4. Determine the following derivatives without simplifying either before or after. (YOU MAY USE ANY…

A: Using given formula then solve it.

Q: 2. Find the derivative of the following functions: 3 + cot x (d). g(x) 3 – cot x

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Q: Find the derivative of the following functions using the definition of the sine and cosine function.…

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Q: 6. Use the rules of differentiation to find the derivatives of the following functions. Do not…

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Q: Find the derivatives of the following functions using the rules of differentiation. Simplify your…

A: Since you have asked multiple part question as per guide line we will solve the First three sub part…

Q: (a) Find the first 4 derivatives of f (x) = sin (ax), and use the results to find the following…

A: The given function is Taking derivative of the function by chain rule

Q: Q1. Find ý of the function x? – e2x+3y – In(xy3) = 0. %3D Q2. Use the definition of the derivative…

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Q: 3. 4ln(Arctan x) = 1- y

A: To find out the double derivative.

Q: 6. Find the derivative of the following (express answer in simplest form): 1+ sinx a. f(x) = In…

A: Topic = Derivative

Q: a. Using the definition of differentiation, find the derivative of the following function Tv Note:…

A: By the definition , differentiation is , f'x = limh→0fx+h-fxh Here ,                       fx =…

Q: Determine the third derivative of y = In(2x + 3) Determine the third derivative of y = e(-x²/2)

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Q: 3. Find the derivative of the following functions using the definition of the sine and cosine…

A: In the question it is asked to calculate the derivative of f(x)=cos(x)sin(x) using the definition of…

Q: B. Find the derivative of the following functions, then use the derivatives to find the equation of…

A: f(x)=2x+3 at the points x=-1 and x=2

Q: A2) Find the derivative of the following functions: x2 + 2 (a). f(x) x2 – 2 (b). f(x) = 2 tan-1(x) –…

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Q: 1. H(w) = 2 cos(w) – 6 sec(w) + 3 H'(w) = %3D

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Q: 15. Find the derivatives of the following functions: (a) = 20 sin 15x; (b) - tan' x: (c)-" c cos x…

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Q: d 10.(4* tan x) dx

A: Find the derivative

Q: Use the new derivative shorteut formulas below to calculate the derivatives of the following…

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Q: 3. Find the first derivative for the following function. Do not simplify . 1+ cot(x) (a) f(x) = (2x²…

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Q: Find the derivative with respect to the independent variable. f(x) = cos ? (8x2 - 1) f'(x) = D %3D

A: Given expression: fx=cos28x2-1 In such type of problem we will apply function of function rule: If…

Q: A2) Find the derivative of the following functions: 1² + 4 (a). f(x) = 1² – 4 (b). f(x) = 2 tan (x)…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: 2. Find the derivative of the following functions: -2 (a). f(x) = x² + 4x + 4e" (b). f(x) = 2…

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Q: A2) Find the derivative of the following functions: x² + 4 (a). f(x) x2 - 4 (b). f(x) = 2 tan-'(x) –…

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Q: 4 Y= 5/(sin3x +cos3x)

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Q: 5. e(2x- y) = 2x - y

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Q: 5. Use the rules of differentiation that we learned in class to find the first derivative of each of…

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Q: Find the derivative of f (w) = 6 ln (w) + 15. Enclose arguments of functions, numerators, and…

A: f(w) = 6ln(w) + 15  Differentiating both sides w.r.t x, we get,

Q: h of the following functions, find the indicated derivative using the de x + cos(3nx) '; f'(1) x2

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Q: 1-x Find the derivatives of the following functions sinh' 1+x

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Q: Using differentiation formulas, write the derivative with respect to x of the following. Find the…

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