Find the derivative of f (z) = -9 . 7². Enclose arguments of functions, numerators, and denominators in parentheses. For example, sin (2x) or (a – b)/ (1+n). f' (2) = You can see, from this problem, why a base of e is more "natural" to use than any other base.

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y= ln x3

A: Given:

Q: Use the General Power Rule where appropriate to find the derivative of the following functions.

A: We have to find the derivative of the function: y=lnx3+1π We know that lnam=m lna Therefore given…

Q: Find the derivative of function.

A: Find the derivative of function. y=(ln|x+1|)4

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: Find the second derivative for the functions defined as follows.h(x) = x/ex

A: Given:             f(x)=xex

Q: (1) Using the definition of derivative, find the derivative of th following functions: (a) y = xvx²…

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: Here the given function  hx=x+2, c=-2 The function can be written as hx=x+2,x≥-2-x-2,x≤-2

Q: Find the derivative of function.

A: The given function is f(x) = ln(xex+2).We have to find the derivative of this function with respect…

Q: 2х- 3 3. У3 5x +1

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Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 (1/2)θ

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Q: y = In- e 2x+1

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Q: Find the derivative of y with respect to x of y = xlnx – x.

A: Using rules of differentiation.

Q: 2) Let y = xe* and find the first derivative y'. Where is y'>0?What does this tell you about the…

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Q: 2) Find nth derivative of the following function f(x) = ex

A: Given query is to find the nth derivative of the expression.

Q: y = x*(1 – In x4)

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Q: Find the derivative of the function.

A: Given that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = ln (3te-t)

A: We expand the function using the properties of logarithm

Q: find the derivative of y with respect to the appropriatevariable. y = cos-1 (x2)

A: Given function is y=cos-1x2. Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: 3. Calculate the derivative of the following functions. For this problem only, do not simplify your…

A: Given:          y=lnx2esin2x              =2lnxesin2x   differentiating on both sides…

Q: Find the derivative of y with respect to x.

A: Assume z=x^5+1. Then found derivative dy/dx using the chain rule.

Q: 4. Find the second derivative of Y with respect to x for 4x² + 8y² = 36

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Q: 10)Find the first derivative or f’(x) of the following functions using long method derivatives

A: We need to find derivative of given function.

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (x2 ln x)4

A:

Q: Find the derivative of the function. 10 f(x) = 3 + 2cos x

A: Recall: dxndx=n xn-1 d(cos ax)dx= a(- sin ax) dc1f(x)±c2 g(x) dx= c1d[f(x)]dx± c2d[g(x)]dx

Q: Determine the derivative of g ( x ) = 3 e-4 x*sin(7 x) with respect to x. = (x), 6

A: As per the guidelines, we need to author the 1st question.  We know that product rule is given by…

Q: Find the derivative of the following function at the indicated point from the graph of y=​f(x)…

A: Find the derivative at the given point

Q: 1+ cos x y = In 1-cos x

A: This question is based on chain rule differentiation.

Q: 1. x² - 2xy + y² − 6x + 2 = 0

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = x4/4 ln x - x4/16

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Q: Find the derivative of the function. y = tan−1 (square root of x - 4)

A: Consider the given function. y=tan-1x-4 The objective of the problem is to find the derivative of…

Q: 5. y³ = 4(y + x²)

A:

Q: Find the derivative of the function. h(e)- (-1) ( 1) +]

A: Given ht=t4-15t3+16

Q: 2. Find the derivative of the function. y = e* In (sinæ)

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Q: Find the derivative of the function y=cos(3 In x).

A: Given y=cos(3lnx)

Q: y = cof'/ x2-1 x²+

A:

Q: Find the 4th derivative of x^10 evaluated at x=0. What would be the 100th derivative of x^2000 be at…

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A: NOTE: Refresh your page if you can't see any equations. . the given equation is take x=-6

Q: 2. If f (x) = xV x + 3, find the derivative of this function and the slope of the tangent line at…

A: Product rule of differentiation: (fg)'=fg'+gf' The slope of a tangent line at (a,b) is given by:…

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

A:

Q: 3. Find the second derivative using implicit differentiation x² + y? = 4

A: Given that x2+y2=4To find implicit differentiation

Q: Find the derivative of the function. simply if possible y = arccos(e2x)

A: We have to find the derivative of the function: y=cos-1e2x We know the formula of derivatives,…

Q: find the derivative of y with respect to x, t, orθ, as appropriate. y = ln (cos2 θ)

A:

Q: find the derivative of y with respect to the appropriatevariable. y = csch-1 2θ

A: Given, y=csch-12θ

Q: find the derivative of y with respect to the appropriatevariable. y = csc-1 x/2

A: We have to find derivative of y with respect to the appropriate variable: y=cosec-1x2 Rewriting the…

Q: -5

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Q: Find the derivative of the function. h(x) = x² arctan(8x)

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Q: Find the derivative of the function. h(x) = ets. - x + 1

A: Differentiate w.r.t x

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = (cos θ) ln (2θ + 2)

A: