consider the following functions. 1₁₂√2: R²DR ول وال S₁ ( x₁, x ₂) = Lop [x₁) exp(x₂) + sin (X₁) Sec (X2) d₂ ( x ₁ ₁ X₂) = x ³₁ x ₂ - 4x, X2 3 2 = [X₂] Let x = Ⓒ) Let 8(x)=[++ (x)]. Compute of.. эх dimensions are correct £2 2 (X) Make sure your 3) Now let x₁ = t ²-3t+1 and x = 2 t3 Compute 2x. Make sure dimension 2+ is Correct your

Q: (2) Find the derivative of each of the following functions (a) f(x) = (1+x*)²/3 (b) g(x) = V1+…

A: a) We use the power rule and chain rule

Q: 1. Find the derivative of the following 9x²-4x+9 a)y = 2(x²-3)²√√3x-1

A: We know that the derivative of a function fx is the rate of change of that function with respect to…

Q: If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as…

A: It is given that, if a polynomial p(x) can be factored as a product of two lower degree polynomials…

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

A:

Q: (В) f (x) 3 3 sin(2x) — 4

A: we have to draw the curve of the function fx=3sin2x-4 let y=f(x). therefore, y=fxy=3sin2x-4 the…

Q: 5. Consider the function f(x). f(x) = (2x² + 3x + 1 |x| sin(x - 1) + 1 if x < -1 if -1 < x < 1 if 1…

A:

Q: 1. Determine the slope of the following functions. į. f(x) = 4x³ + 5x4 - 9x + 2 f(x) = sin(3x) - 5x³…

A: We determine the slope of the following functions.                          i. f(x) = 4x3 + 5x4 - 9x…

Q: Find the derivative y = √√x S 3t cos (16) dt 0 A. 3 cos (x³) -3√√x sin (x³) OB. 3√√x cos (x³) OC.…

A:

Q: Find approximate value of the derivative for f(wo)-6f(x1)+3f(x2)+2f(x3) fr(x2) = f(x) = 10 sin(20æ?)…

A: Introduction: Numerical differentiation is the technique of obtaining the numerical value of a…

Q: 2. Find the anti-derivative of a. f(x) = 2x¹ - 5√√x³7−2e* ++ 3 1 1+x²

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

Q: 7. Find the second derivative given g(x) = sin x² A. 2 (cos x² - x sin x²) C. 2x cos x² 9 "(x) - 4 x…

A:

Q: Find for THREE of the following functions: dx 1-y()+In(cos(x)) + √2-y=2(cos(x))*(x)

A:

Q: Find the derivatives – do not simplify a. y= x4- 3square root of x + 5x2/3 +8/x-3

A: ddxxn=n xn-1

Q: 2) Find the derivative of the following function 1² +5 1² – 5 (a). f(x) = (b). f(x) = 2 tan '(x) –…

A:

Q: 5. Let the derivative of the function f(r) be novin at dad FOLL 11 g(x)=x+ sin(x - 2) and ƒ(2+)-f(2)…

A:

Q: 2. Use the derivative rules to find f (x). (a) f(x) = (2x® – 8x-2 + 9) +) 3 (b) f(x) = COS x CSCX_…

A: Find the derivative

Q: 1. Find the natural domain and the derivative of the given function. (a) 3x² +7x + 5, (b) (3x +1)5,…

A:

Q: 2. What is the second derivative of f(x) = - ²x³²x²+6? f"(x) = 5x² - ²³√x f"(x) = 10x + √√√x+6 a. b.…

A:

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

A:

Q: O Find the derivative of the following functions: L 2+3 (a). f(z) = 2-3 (b). f(z) = 2 tan (z) – 7…

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

Q: Find the derivative of the following. a) y = cos (4x³ + x²-2) b) Y=xsin ''(x) + √√1-x²

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Q: 7. Find the second derivative given g(x) = sin x² A. 2(cos x? – x sin x?) B. 2(cos x? – 2x² sin x²)…

A:

Q: . Express the function F(x) = 1 + sin x 1+ sin² x in the form (fog)(x).

A:

Q: 1. Prove that the derivative of tan(x) is sec² (x) directly from the definition of the derivative.…

A: The derivative of fx with respect to x is defined as:limh→0fx+h−fxh

Q: 2. Find the derivative of each function: cos (x) 1-x² (b) g(x) = 5√x - √ (c) f(x) = (3x² + x −…

A: