Find the values of the coefficients a, b and c so that the conditions: f(0)=-2,  f'(0)=-1,  f''(0)=-5 hold for the function f(x)=ae^(-3x)+be^(2x)+cxe^(2x)

Q: Find the solution of the equation y= 2x -x- 10 in the interval (2, 4] using derivatives. You can use…

A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

Q: Solve for the derivative of x² – y² = 9 using implicit differentiation %3D

A: Given :                x2 - y2 = 9To find :                 y'

Q: 3x+4 3. f(x) = x2+3

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Q: FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 2. y = 2 Arccos (1-x/2)+ Square root of…

A: Second order derivative.

Q: At the point (1, 2),the function ƒ(x, y) has a derivative of 2 in the direction toward(2, 2) and a…

A: Consider ∇·f=ai+bj at point (1,2). The expression for the direction towards the (2,2) is, The…

Q: 3x-4 1. y = Arctan

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Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: Solve by Chain Rule (V3x² + In(5X*)) y = tan

A: To differentiate the given function using chain rule.y=tan3x23+ln5x4

Q: f(x) = (6x² - 2x+1)^

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Q: Find  y ″  by implicit differentiation. 2x3 − 5y3 = 5

A: We will differentiate w.r.t x twice using the product rule and the chain rule

Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: Find the Indicated Derivative for Higher-Order 1. y = 10x5 - 21x4 + 13x3 - 6x2 + 5x - 1000 ; y(6)…

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Q: An ant is standing at the point (1,1,3) on the surface of a bowl with equationz=x^2+…

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Q: Find the second derivative of function, and then find ƒ″ (1)  and ƒ″ (−3) .

A: Find first the derivative as shown below: f'x=ddx-5-x2        =125-x2ddx5-x2       =-125-x2-2x…

Q: 1. f(x)= Vx3 + 2x² + 3 2. f(x) = (6x – 7)(2x + 3)

A: To find the second derivatives of the given functions.

Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" :

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Q: Find the derivative of the function. Express it using positive exponents only. y…

A: For power 3, use the power rule. Then use the chain rule

Q: Solve for the derivative of the function using chain rule. 11. f(x)= ln(sin(8x))

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Q: 2 that also passes Write the equation for a quadratic function f(x) with roots at x = 7 and x =…

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Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: Find y" by implicit differentiation. 2x3 + 3y3 = 2 y" =

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Q: if the derivative of x2sinx+2xcosx-sinx  is (Ax2+B)(cos(C(x/2))). FInd the value of A, B, and C.

A: Given: x2sinx+2xcosx-sinx Differentiate the equation.…

Q: Find the first derivative: y = In V2r³ – 5 O y =: 22-5 O y = 4z 22-5 O y = 62 22-5 O y =; 2z-5 O y =…

A: Here we have to find the first derivative of         y = ln(2x3-5)1/3

Q: 1.f(0) = (금x* + 3)" %3D

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Q: Find the derivative of f(x) = (1 + 7x2)(x − x2) in two ways. 1. Product Rule 2.Perform the…

A: For product rule we use u=1+7x^2 and v=x-x^2Product rule = u'v+uv'Answer: f'(x)=1-2x+21x^2-28x^3

Q: 3x+4 3. f(x) = x2+3 12 x3+6x2+3x 4. f(x) = 3x

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Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Given the function y = 8e-2x + 7 sec² 5x - 4 ln x³, find y'. Solution: 4(3)x² 3 12 X ------- 12 1…

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Q: 12 x+6x?+3x 5. f(x) = 3x Vズ-3 6. f(x) = ズー9

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Q: Find the derivative and simplify exy -x² = 4Y² %3D

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Q: Find a function with the given derivative whose graph passes through point P f'(x)= 2xx+1-cosx,…

A: To determine the antiderivative satisfying the given initial condition

Q: Find y''by implicit differentiation. 2x3 + 5y3 = 2

A: We can find y" using implicit differentiation as below.

Q: find the derivative of f(x) = (x²+4)(3x³ – 2x) at the point x = - 3[ use product rule] В I !!

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Q: Find the derivative at the point (0,.5) x2+y2=(2x2+2y2-x

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Q: Determine the second derivative of 2x+ y-- 4 y 6.x (y + 2)--9(y+2) A B - 6x (y+ 2)-+ (y + 2) - 6x (y…

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Q: Find y" by implicit differentiation. 4x3 + 5y3 = 6 У" :

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Q: Find the function ƒ(x) whose derivative is sin x and whose graph passes through the point (0, 2).

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Q: Find the first and second order derivative w=3z7-7z3+21z2

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Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: 9) Find the value of the derivative at the point (2,-18) ƒ(x) = -3xV2x + 5

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Q: Зx+1 5. f(x) %3D 3x2+2

A: f(x)=3x+13x2+2Differentiate…

Q: equation of the function f whose graph passes thro f'(x) = x/25 - x²

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Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

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Q: Determine the second derivative of y = v5x² + 1 Determine the third derivative of y = (x² – 1) (2x3…

A: Second derivative of5x2+1 is  d2dx25x2+1

Q: Find the fourth derivative of the given: (Show complete solution from first to  fourth derivative)…

A: The function is given by y = (2x+1)25

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: 2 12. f (x) = (1tsinx) Cosx

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Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: Find the derivative. USING CHAIN RULE 4 y = V3x² – 5x + 2

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