. Find the inverse of the function f(x) = 1 + (1/x), x* 0. Then show that f(f(x)) = f(f(x)) = x and that df dx f'(x)

Q: Show that is C is a function of x with derivative C'=C/x and N=C/x, the d/dx (C/x)=(C'-B)/x

A:

Q: Find the derivative of y with respect to x. y = tan (In 3x) O A. 1+(In 3x) 21 O B. x(1 + ( In 3x)) 1…

A: Given: The function y=tan-1ln3x, To determine: The derivative of y with respect to x,

Q: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

A: Write down the limit definition of the derivative f'(x) and USE IT to find d/dx(1/x)

Q: Find the first derivative of the following functions with respect to x: a) y= Inx3 b) y = ln (÷) c)…

A: We can make it easier for you.

Q: Consider y = f(x)=√1+2x, x 2-1/2. Without finding x = f(y) explicitly, find the derivative of the…

A:

Q: Find the derivative of the function. 2 a) f(x) = x² ln(x) b) g(x) = 2" + log, (x + 5) +ez c) y =…

A: We have to find the derivative.

Q: The derivative of y= xh* is O 1) (In x)(xh*-) O 2) 2 an x)(xh*) O 3) (In x)* O 4) xhx

A:

Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: Given:        x2+2xy=y3

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

A: We use the chain rule

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y=x" In x - O A. 4x-x O B. x*…

A: The function is given as y=x4 ln(x)-13x3 Differentiate the above function w.r.t 'x' y'x=ddxx4…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y= In (In 5x) O A. 1 5x ОВ. 1 x…

A:

Q: Evaluate the second derivative of e22.1.png acos(b/x) f(x) x2 if a = 323 and b = 0.5 at x = 3 using…

A: Given function is f(x)=323cos0.5xx2 Step value is ∆x=0.1

Q: Find the derivative of the functions below: In(x) (a) g(x) = log,(x) g'(x) = (b). y- in(6x®)

A:

Q: S-2(x-1 - x²) dx 5.

A:

Q: Find the derivative of the given function. 5x y= In 6+x dy dx

A:

Q: Find the derivative of the function y = In(8 – e-a f'(x) =

A: We have to find derivative

Q: Find the derivative of the function

A: Given function, Fx=∫πlnxcoset dt

Q: Evaluate the function: S de x(x-2) -dx (x–1)³

A:

Q: Evaluate the derivative of indicated order of the following functions: d2 (x cos(x² + 3x) а. dx2 d…

A:

Q: f. y=In(x8+1)

A: We will solve the problem

Q: Find the derivative of the function. F(x) = In(4 – x®) %3D f'(x) %D

A:

Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

Q: Find the derivative of the following function. y= In (x3 + 2) * dy dx

A:

Q: Obtain the derivative of the function y y = (e*1) (In(2cos(x² – 4x))

A: The given function is: y=e3x+1ln2cosx2-4x

Q: 3 Find the derivative of the inverse of f(x) = x +1 using the formula dy %3D 1 off "(x)= g'(x)= dx…

A:

Q: - Use integration by parts to show that if f has an inverse with continuous first derivative, then…

A:

Q: 1. Find the anti-derivative of the following. e" (x + 1) dx x2

A: From the given information. Anti-derivative has to be calculated to the following expression.

Q: Find the derivative of the function f (x) = /e* – In(x) 12 – 1/x) O (ex12 – 1) O (e2 – 1/x) e? -x)

A:

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

A:

Q: Suppose In (x + 2y) = xª. Use implicit differentiation to find the derivative of y with respect to…

A:

Q: Let y = In(x'e2x ). Find dy/dx.

A:

Q: Find the derivative of the inverse of f(x) = x' +1 using the formula dy 1 * of f"(x) = g'(x) = dx…

A:

Q: Find the derivative of the function f(x) = Jet – In(/x) (e+12 – 1) O (e:/2 – 1/x)

A:

Q: Compute the derivative d/dx of the following functions: f(x) = x cos^2(4x)

A: The given function is: fx=xcos24x   As we know that; The Product rule: f·g'=f'·g+f·g' The Chain…

Q: If f (x) = In (4a + 1), then its third derivative is f(3) (æ) = %3D

A: In this question, concept of derivative is applied. Derivative The derivative expresses the rate of…

Q: Let y = f(x), where   f(x) = 5x3/2 + x1/2.   Find the differential of the function.

A: The given function is

Q: Find the derivative of each function e 2x a. f(x) = 2x+1 b. f(x) = In Vx + 2x %3D c. f(x)= x?e* – 6x…

A:

Q: Find the derivative of the function. f(x) = 2 tan (e11x) f'(x)=D

A: We have to use Chain rule of differentiation.

Q: Find the first derivative of g(x) if g(x) = e²* In(2x) %3D

A:

Q: Evaluate the second derivative of e22.1.png acos(b/x) f(x) = x2 if a = 149 and b = 0.3 at x = 3…

A:

Q: 4) /() =2-2 3. 5) y = x*+2x+1 6.) f(x) =

A:

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

A: Given that: b. f(x)=lne5x(2x+1)5x2+1c. f(x)=(xlnx-x)

Q: Find the second derivative of y with respect to x if y = x In(x) - X. А.X In(x) B. In(x) C. In(x)/x…

A: The given function is y=x ln(x)-x

Q: Find the derivative. COSx a) f(x) = In %3D x2-4 4 b) g(x) = Vx + e2x + Tt

A: Given : (a) f(x)=ln(cosxx2−4)

Q: Integrate the following functions f(x)=Ln [sec (x)] [², 3]

A: We will see the graph of secx to judge the value of greatest integer function of secx.

Q: Find the derivative with respect to x of h(x) = e2x²+6 In(x).

A:

Q: The derivative of f(z) = Log(2iz - 4+6i) at z = -3+i is

A:

Q: Compute the derivatives of the given functions. a) f(x) = 3 ln x. f'(x) = b) g(x) = In(x*). g(x) =

A: Given f(x)=3lnx now we need to calculate the derivative of f(x) f'(x)=ddx(3lnx)=3ddx(lnx) deriative…

Q: Use implicit differentiation to prove that d/dx [ xn ] = nxn − 1

A: Here we use implict differentiating to prove thatddxxn = nxn-1

Q: Compute the derivative of the given function. f (x) 10x-1/4 cos e + 7 sin a %3D -

A: