Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

Q: Find the derivative of f(x) = COS 4 log3 (x²) os(5x)

A: Explanation of the answer is as follows

Q: Find the derivative using the chain rule: x(x^2+1)^(-1/2)

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Q: Evaluate the derivative of y = cos '2x - In 1-4x, where x = 0.125 -12> 2

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Q: Find the function whose derivative is 1-e2x

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Q: Find the derivative of g(x) = (cos(8x))3

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Q: Find the first derivative of y = e3x. 3e3x

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Q: 5. Find the derivative of: a. f(x) = cos(e³x-4)

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Q: Find the derivative of the function.

A: Use the chain and quotient rule of derivative to differentiate the function.

Q: Find the 50th derivative of y = cos 2x

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Q: Find the derivatives of the functions defined as . y = -6x sin 2x

A: Given: y=-6xsin2x Now differentiate the given function, we get, dydx=ddx-6xsin2x⇒dydx=-6ddxxsin2x…

Q: Find the derivative of: 9e 7sin ( 3x*) Use e^x for e". -

A: We use chain rule to find the derivative.

Q: 1) Find the derivative of y =-+x-1 %3D

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Q: 3x-x Tan 1-3x? х-х

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Q: Find the derivative of k(x) = log3(x) cos

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Q: Find the derivatives of the functions in Exercis y = (1 + 2x)e-2x

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Q: What is the derivative of y=cos3(5x)

A: To find the derivative of: y=cos3(5x) For that use chain rule and ddx(xn)=nxn-1ddx(cos x)=-sin x

Q: Shows the derivative function of: e3x+5

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Q: 10. f(x) = cos (2x)e*²-1

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Q: Find the first three derivatives of y = x(In x)³

A: given problem :y=xlnx3

Q: Find the 75th derivative of y=cos(2x)

A: Given function y=cos2x The 75th derivative has to be founded  first consider the smaller…

Q: Find the derivatives of the functions y = (3 + cos3 3x)-1/3

A: Given that, y=3+cos33x-13

Q: FInd the derivatives of the function f(x) from the first pribnciple  cos2x

A: Derivative from first principal is ratio of change in y to the very small chance in x.

Q: Find the derivative of the function. y = In(12x)

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Q: 2х Find the second orfer derivatives of y=Tan" 1-x3

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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 second derivative of f(x) * f(x) = cos² 7x

A: The given function is: fx=cos27x   As we know that; The Chain Rule: fgx'=f'gx·g'x The Product Rule:…

Q: Find the derivative. [미 In dx x +3 x-3

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Q: Find the First Derivative of the Given Function: 2.) x=sec53t

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Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: 3. = 2x-y х+3у

A: We will differentiate the given problem with respect to x.

Q: Find the derivative of function.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

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Q: Calculus 11th Edition - Ron Larson Please assist with the question below. Please show &…

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Q: Find tte implicit derivatives of the (x-y)3 = (x+y)2

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Q: Find the 50th derivative of y = cos(3x)

A: Zeroth derivative y = cos(3x)First derivativey' = -3sin(3x)Second derivativey''=-9cos(3x)

Q: Calculate the first derivatives of ƒ(x) = x2/(x2 + 1) and g(x) = -1/(x2 + 1). What can you conclude…

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Q: Find the derivatives of the functions defined as . y = cos4 x

A: Given function, y = cos4 x

Q: 3. Find the derivative of h()= 5²°-2z-1 %3D

A: We have to find derivative

Q: Find the 85th derivative of y = cos(3x).

A: Do the derivative many times and observe the pattern that derivative follows. Generalized it and…

Q: Find the derivative of f(x) = 4e 3x + e -x^2 f(x)= ?

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Q: Find the derivative of y=cos-1 (19x)

A: Consider the given function, y=cos-119x it can be written as, cosy=19x

Q: Compute the derivative of f(x) = arcsin(x² e3=).

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Q: What is the derivative of y = etan-1 2x 2

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Q: -5

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Q: 8. Find the derivative of y = In(3t) dt.

A: To Determine: Find the derivative of given integral:…

Q: Find the first derivative of x² + 3xy + y3 = 10 implicitly.

A: The given function x2+3xy+y3=10

Q: Compute the derivative of f (x) : = arcsin(x² e³«).

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Q: In x g(x) = 2

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: