If r=xi-yj+zk and r= r|, prove that for differentiable function f(r) d'f 2 df show that vifr) = dr and hence find f(r) such that V?f(r)=0. r dr

Q: f(x,y,z) be a differentiable function the point P(2,5,-1). Let at Which of the following is the…

A: Answer is mentioned below

Q: Determine the x-coordinate of the point for which the tangent is horizo Function f(x)-¹. X A) 3 B)…

A: Determine the x- coordinate of the point for which the tangent is horizontal to the function

Q: 5) Let f be differentiable at a. Show that f(z) is differentiable at a if and only if f' (a) = 0.

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Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: Why is the function f(x)= cotx not differentiable on the interval [0, pi] ?

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Q: Let z be a differentiable function of x and y related by the equation: x z ++* =(√√y+cosh(z))". X 2…

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Q: Is there a twice differentiable function f R2R whose best adratic approximation at the point (1,0)…

A: Given problem is from differential calculus in several variables. We have shown that there exists a…

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: of lf" (x) [0,2] f(x)=√1+x² HINT: Much like the previous question except that you are focussing only…

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Q: Check that the equation x³ + y³ + z³ = x + y + z implicitly defines at least one differentiable…

A: Solution

Q: (z)dz

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Q: .. Find the absolute extrema of the function with its corresponding constrain. a) f(x, y) = x² - y²;…

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Q: Determine if f(x, y) = xe*-y + 100y is increasing or decreasing at (-2,1) if a) we allow x to vary…

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Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: Let f be a differentiable function with f(1) = -3, f'(1) =0, and 1+ f(x) h(x) = What is h' (1)?…

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Q: Assume that the functions ?,?,ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c,…

A: given: ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c, h′(c)=d, f(a)=e, g(e)=ℓ,…

Q: F is a differentiable function of two variables, x and y, such that Fx (0, − 2) = −4 and F₁(0, − 2)…

A: Given z=F(tan(u-2v+5), u3v)To find: ∂Z∂u

Q: Let f(z) be a differentiable function on the interval [-6, 2] such that f(-6) = --4 and f'(z) < 2.…

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Q: Using the CRE Theorem, find and sketch the set of all points zo = xo + iyo where f(z) = z² + 2|2|² +…

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Q: Let fbe adifferentiable function satisfying the condition. f(x) for all x, y (+0) ERand f(y)#0. f(y)…

A: Let f be differentiable function satisfying the condition Given f(xy)=f(x)f(y)put…

Q: Find the interval(s) where f is concave up for f(x) -4x4-3x- 5x-10 0)

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Q: Find the analytic function where real part is e*(x siny – y cosy).

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Q: If x= f(u, v), y = g(u, v), u = D(r,s), and v=Y(r,s) are differentiable functions then prove that…

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Q: Given the function: f(x,y) = 4x*y² – 10p +y , find f a. 16x'y-60xy O b. 48x°y O C. 16xy – 10y O d.…

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Q: If [3-2 fro] dse =15 Then

A: Evaluation of the definite Integrals,   by using properties of the definite Integral

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: