Given the two functions h(x) = log, (z) +3 and g(2) = 42z +1. The domain of k(z) = (h°g)(x) is

Q: 2. Ifƒ (x, y) = log (x² + y²), then ƒ +ƒ is equal to XX yy 1 (a) x² + y² (b) 0 1,² - x² (c) (d) *…

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Q: The problrm is to Find the indicated derivatives.

A: (a) The given function is ,

Q: In the given question/s , find the derivative of the function. h(x)= ln (2x2 +1)

A: Given, h(x)= ln (2x2 +1)

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

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Q: What is the derivative of e7 ** (4 x*+11)3 y = (16 x2+8 x-5)5 vith respect to x? Hint: Take the…

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Q: Provide the equation of the line tangent to the given function at the specified point g(x)=ln(x^2);…

A: Given : gx = lnx2

Q: Find the derivative of f(x) = In(e +4) 1 O 3e? e+4 3e3

A: We use the chain rule

Q: | (r log x)² dz,

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Q3/ find the derivative D f(x) = x log5 @f(x) = (x+3) ² 2x+4 2 X

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Q: Find the derivative of the following function using logarithm laws. (2x2 + 3) y = (x – 1)2

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Q: | 1-x² y = log10 2- 5x

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Q: Find , given y = log(ev+x²). dy dx

A: Given y=logex+x2  We find dydx The differentiation formula of logarithm is ddxlnx=1x and the power…

Q: -e' 4. Y = e3x +e¬3X

A: Given: y=e3x-e-3xe3x+e-3x

Q: -g(y) + C log(z)

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Q: S-2(x-1 - x²) dx 5.

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Q: Compute the given derivative. dx x=-9 e 1/9 O 9e9

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Q: Find an equation of the tangent line to the graph of the function  y = log3 x, at the given point…

A: y = log3 x

Q: Solve the following equations (a) ez = 2i (b) log (z2 -1) = i/2

A: We have to solve the given  complex equations .

Q: 3. Find the first derivative of k(x) if k(x) = e(4x – 3)

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Q: e3x-e-3x Y = e 3x+e-3x 4. t2 y= 72-1 5. X = t-1

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Q: Find graphically approximate value of the root of the equation an 3 – x = e* - 1.

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Q: y = log, x is equivalent to the exponential form %3D x > 0, b > 0, b # 1.

A: To fill in the blanks

Q: Which of the following is a linear equation? O log 20 + e 1 O 2z + 3y- 1 O log a- log r+y= 3 O sin z…

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Q: Consider the function f (x) = log10 x.  Find the ratio of x1 to x2 given that f (x1 ) = 3n and f (x2…

A: Given, f(x)=log10x To find the ratio of x1 to x2 given that f (x1 ) = 3n and f (x2 ) = n.

Q: At what value(s) of x does e^(-x2) =x2 - x + 1?

A: To determine the values of x at which,

Q: 6. Find the derivative for each function. b. f(x) In 5x3 2)3 f(x) (e*3 2) а.

A: Use exponent rule for exponent 3 and use chain rule for (e^x^3 +2)

Q: What is the derivative of (9x² + 14)2 (20x2 +11a- 15)3 123 e y = with respect to x? Hint: Take the…

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Q: Find The Domain of the Function. y = sin(log, x²]

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Q: If x = e*-Y then is equal to A) B) log z (1+log z)* C)

A: solution:-xy=ex-ytake log both sideslnxy=lnex-yylnx=x-ydifferentiate both sides w.r.t…

Q: Find h" (x) if h(x) = log,(cos(x)) – e®z. -

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Q: e: Sz dx (x+1) log(x+1)

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Q: A Disguised Form of the log Rule, Find

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Q: As picture sho w

A: We need to find the derivatives of the given expression.

Q: find the second derivative and simplify the final result 10. y= (e^(-3x+4) +2) / (e^(2+3x) +1)

A: Given that, y=e-3x+4+2e3x+2+1 We have to find the second derivative of y with respect to x.

Q: x-1 y = log XArctanx - Invx2 +1 = y x+1

A: We can find the second derivative as below

Q: Find the first derivative of each of the following: a. y= 15x + 4x° – 6x + 8 b. f(x) = x³ e* 3 c.…

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Q: Given that the equation of the RED line: y = log,(x) 15) what is the equation of the BLUE dotted…

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Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: FInd the Domain of these functions. f(x) = log7 (4x + 8) f(x) = ln(4x − 20)

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Q: d. m(x) = log,(x + 3) e. n(x) = e' = e*- a.

A: Given- d.  mx=log4x+3 and e.   nx=ex-1 To Find- The domain and range of the above functions.

Q: Find the range of the function x* +e x+e f(x)%3sin{log, +cos {log. x' +1 2 x*+1

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Q: 2) Write the derivatives of these four functions: a) 7 log8(x) b) 3ex c) 5(16x) d) 9ln(x)

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Q: 2. Find the derivatives of the following functions. a) y = (log2 x)3¬*

A: Given information: The function is y=log2x3-x. Calculation: Find the derivative of the function. Use…

Q: Consider the equation M, = - log10(E) – 10.7 relating the moment magnitude of an earthquake and the…

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Q: y = log,(x + 3)

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Q: Find the derivative of the given function. e5x (2x+1)5 f(x) = In Vx2+1

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Q: 1- Find the first derivative of y with respect to x for the following functions: In5 7x y = log5 . a…

A: