Differentiate f(w) = sinw + w²tan-1w

Q: Compute the derivative of f(t) = (3t2 + sin t, cos3 t + 8t2, 5tan t) relative to t.

A: d(u+v)/dt=  du/dt + dv/dt

Q: Find the directional derivative of z = f (x, y) = x²y³ – 3y² at (-3,4) in the direction of the…

A: Use directional derivative formula which is mentioned in solution.

Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx point (1,-1,1) in the direction 3i+4k x at…

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Q: Calculate the derivative 24 dt using Part 2 of the Fundamental Theorem of Calculus. a va a sin (a)

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Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Use the intermediate Value Theorem to show that between x = 0 and x = 1, the function f(x) = 3 sinh…

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Q: Use Part 1 of the Fundamental Theorem of Calculus tofind the derivative of the function.

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Q: Find the derivative of f(x) f(x)= integral 1 to sinx of (1+t^3)^(1/4)dt

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Q: Find the directional derivative of f(x, y) = x² sin(2y) at (1, 7/2) in the direction of ở = 3i– 4j.

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Q: Calculate the derivative of f (x) = cos (7æ³ + 2) %3D showing all your work.

A: Topic-derrivative

Q: Find the third derivative of ƒ (z) = VT2z+I. f" (z) =

A: We use the exponent rule and chain rule.

Q: 3. Prove that the directional derivative of f(x, y) = y² + 2xy³ + x³y² at point (0.1) in the…

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Q: Find the direction derivative of f(x, y, z) = x²y - zx -yx point (1,-1,1) in the direction 3i+4k %3D…

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Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of F(x) = / sin (t*) dt…

A: Use part I of the Fundamental Theorem

Q: Find the derivative of F(x) = 4 sin(t) dt. 3x %3D dx cos(x)

A: Solve the following

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. cOS X y =…

A: To use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.y=∫sin…

Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: Find the derivative of ƒ(x, y) = xey + cos (xy) at the point (2, 0) in the direction of v = 3i - 4j.

A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

Q: Find the derivative. F(t) = In(sinh(2t)) %3D F'(t) %3D

A: Find the derivative of the function

Q: fro(x- dt show that = f(x). dx y 3

A: y=12∫0xft x-t2 dt

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) 5t…

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Q: Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

A: The solution is given as

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 0. y = 3…

A: Given, y=∫ex03 sin2(t)dt  We need to calculate the value of y' It is of the form of…

Q: Find the derivative of f (x y z) = x^3 − xy^2 − z at (1, 1, 0) P0 in the direction of A = 2i - 3j +…

A: Given,           f(xyz)=x3−xy2−z  and point Po =(1,1,0) and the direction vector A=2i-3j+6k.

Q: Find the linearization of ƒ(x) = √(1 + x) + sin x - 0.5 at x = 0.

A: substitute 0 for x in f(x)=1+x+sin x-0.5 to obtain the value of f(x) at x=0 f(x)=1+x+sin…

Q: Assuming y cos (3xz) = 5 defines z as a function of x and y. Differentiate

A: we have to derivative

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan x y =…

A: According to the Fundamental Theorem of Calculus, If gx=∫axftdt , then g'x=fx Consider the given…

Q: f(x) = 2x² cos(r®)

A: Given Data: Function: f(x) = 2x2 cos(x5)   The product rule of differentiation is,

Q: Calculate the derivative d dz (2t5 34 dt using Part 2 of the Fundamental Theorem of Calculus.

A: The solution are next step

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of 3z F(x) = | cos (t°) dt.…

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of f(x) = V +2*dt %3D…

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Q: Let sin(r-y) ||| + \y| +0 (x, y) = (0, 0) f(x, y) Is f continues at the origin? Why?

A: Solved below

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y = |. 5…

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Q: Find f'(x)'f f (x)= arctan (Inx) %3D

A: Using composite function formula.

Q: 9. Find the directional derivative of f(x, y) = 3x² – y² + 5xy at (2,–1) in the direction of -3i –…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. g(v) = '…

A: We will use the fundamental theorem to find the derivative

Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

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Q: Find the directional derivative of f(x,y) v = 3i – 4j. x² sin 2y at (1, 7/2) in the direction of |

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: Verify the differentiation formula.

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. h (x) =…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y = 2 sin3…

A: We can use fundamental theorem of calculus in order to solve the given problem.

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of F(æ) = | sin(t) dt F'(x)…

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. y g(y)…

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Q: Find the derivative using the First Fundamental Theorem of Calculus. 13)음 V8t +7 dt dx

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Q: find the directional derivative of f (X, 4) = 3x² + 5y² at the poin t (1,-1) in the dccection of V…

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Q: cos z dz ar gral f

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Q: dy by implicit differentiation of 2r2 3y2 = 4?

A: