Find the derivative of the function. f (x) = 4/3 Squareroot x + 4 cos x Rewrite the function f(x) using an exponential expression for the radical. f(x) = 4x times+ 4cos x

Q: 9.) f(x) = (2x+ 1) 10.) f(x) = x2

A: Given: f(x)= (2x+)2 f(x) = x-2

Q: Find the second derivative of the function. f(x) = e−3x + e4x

A: Given below the detailed solution

Q: Consider the following. 8x f(x) x2 Find the derivative of the function. f'(x) = Find the slope m…

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Q: Find the derivative of y = (-4x - 9)csc (x). Be sure to include parentheses around the arguments of…

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Q: 2. Find the derivative. Simplify where possible. (b) у %3 tanh-1(г3)

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Q: Find the derivative of the function.  s(x) = sq root of x + 7 /  sq root of x         Find the…

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Q: Find the derivative of the function. g(x) = 6e√x g'(x) =

A: Given that g(x) = 6e^(√x) We have to find the derivative of the function.

Q: x-2 Find the 1st derivative of y= sin x+3

A: To find the first derivative of y=sinx-2x+3. Solution: Chain rule of differentiation states that:…

Q: f(x) = 10x^(3) + 8x^(2) + 9x - 6x when the entire problen is divided by x    find the derivative…

A: f(x) = 10x^(3) + 8x^(2) + 9x - 6x when the entire problem is divided by x

Q: (1) Using the definition of derivative, find the derivative of the following functions: (a) y = xVx2…

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

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Q: ln(x+(x2 −16)^(1/2)) Find the domain and the derivative of the function.

A: Given, function is

Q: + 4x" + 4х 3D0.

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Q: Find the derivative of the function f. 3 √√x If your answer has a radical, express it as a rational…

A: solution:-f(x)=3xf'(x)=ddx3x        =3ddxx-1/2        =3-12x-12-1        =-32x-32         =-32x32…

Q: Find the derivative of the exponential function. y = e5x tan(5x)

A: given that  y =e5x  tan(5x)  So dy/dx=e5x d/dx(tan 5x)+tan (5x). d/dx(e5x)                 i.e…

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: Calculate the derivative. y = x4 - 4 x² 5 (Give an exact answer. Use symbolic notation and fractions…

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Q: Find the derivative of the function. h(x) = log2(x2 + x)

A: Given function is : hx=log2x2+x To find the differentiation of a given function.

Q: What is the derivative of f(x) · g (x) in terms of f g? -1 Compute the derivative of -sin(x) · 2x…

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Q: Find the derivative of the function at P, in the direction of A. f(x,y) — - Зху + 4y*, Po(-6, - 5),…

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Q: H(x)= x^5 arctan 5x find the derivative of the function

A: The given function is,

Q: cos (x) V3x² + 7 (3x + 1)5 /2x + 5 7. Use logarithmic differentiation to find the derivative of f(x)…

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Q: x²+x+4 What is the first derivative of r(x) = log, x°cos x

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Q: e* (x+2)' /3x-5 Use logarithmic differentiation to find the derivative of the function. f (x) = -3x

A: Given, fx=e-3xx+253x-56 Let y=fx ⇒y=e-3xx+253x-56⇒y3x-516=e-3xx+25 Taking logarithm on both sides…

Q: a) Find first and second derivatives of the following functions: x³ + 7x y=-cot(3t-1)

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Q: Vx+2 Use logarithmic differentiation to find the derivative of the function. f(x)=- e (3x-1) i ora…

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Q: find the derivative of f(x)=x^6e^xcos(x) use symbolic notation and fractions where needed

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Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOLUTION): e2x –…

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Q: Find the derivative of y with respect to x. (x-y)^2=2ax

A: The given function is: (x-y)2=2ax To find the derivative of y w.r.t. x.

Q: 2. y = a Cos-1 (1 -2) + V2аx — х2 a

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Q: Find the derivative of the function g(x) 4 – 2x g'(x)

A: We have to find the derivative of the function g(x)

Q: Find the derivative of the function in (a). Find the derivative of the function in (b) Or show…

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Q: Determine the derivative of x2 + 2xy + y? = 10 implicitly. Determine the derivative of y sin x = x³…

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Q: 5.) f (x) = 2x² – 3x – 5 Зх —

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Q: Find the derivative of the function at Po in the direction of A f(x.y) = 2xy + y², Po(-6, - 4), A= -…

A: The given function is : f(x,y)=2xy+y2, P0(-6,-4),A=-2i-2j.

Q: Find the derivative of the function at Po in the direction of A. f(x.y) = 5xy- 5y", Po(-7,-2), A= -…

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Q: x d) f(x) = x² sin - R e) f(x) = x+₂ x-2

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Q: b. TRUE or FALSE. It is appropriate to use the chain rule to find the derivative of the function f…

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Q: Find the derivative of the function.  g(x) = x−2 − 9x−1 − 4   g'(x)=

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Q: Find the derivative of the function below. (Do not simplify your answers, and SHOW ALL STEPS) 3x5 +…

A: Use the concept of the derivative of the form  f=u/v

Q: Use the product rule to find the derivative of (82° – 3x*) (7e" – 1) Use e^x for e". You do not need…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: (x²+1)* Find the derivative with respect to x: y = In /1-x

A: The given function is: y=lnx2+151-x

Q: Find the second derivative

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Q: (a) Find the second derivative of the function y = 2x² sin(x). (b) Find the derivative of the…

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Q: x2 + 1 x' + Find the derivative of the function f(x) = In

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Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos*…

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

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Q: (x² + 4)(x – 2)² Vx +7 g(x) = In %3D Find the derivative of this function, g'(x).

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Q: Find the second derivative of the function. f(x) = e−4x + e2x

A: Given query is to find the second derivative fi the expression.