By using the first principle, find the derivative of the following functions. 1.  f (x) = x^2 - x

Q: What is the derivative of x^6

A: We have to use exponent rule.d/dx(x^n)=n*x^(n-1)

Q: Find the derivative of the following functions and simply it whenever possible. y = ln(x+3)4

A: Please see the answer below.

Q: Find the derivative of the function y = 2x sinh−1(2x) − √(1 + 4x2)

A:

Q: Find the derivative of x/ex^2.

A:

Q: Find the 3rd derivative of the function y=xsinx

A:

Q: Find the derivative of the function. 5 F(x) 1 + 4x + x3 F'(x) :

A:

Q: What is the second derivative of f(x)=6x^4 at the point x=−2?

A:

Q: Show that the derivative of the function sinh -¹ x can also be obtained by letting y = sinh -¹ x and…

A: Soln:To find the derivative of sinh-1x

Q: Find the derivative of excosh(x)

A: Topic:- Derivative

Q: show that nth derivative of  f(x)=x^2/(2x+1)(2x+3)

A: nth derivative of f(x)=x2(2x+1)(2x+3) f(x) can be written as by using synthetic division method…

Q: 13. f(x) = e* In x

A:

Q: Obtain the second derivative of the function f(x) = 6 In(8x) – 3z4 and state the value of this…

A:

Q: Find the derivative of the function. Express it using positive exponents only. y…

A: For power 3, use the power rule. Then use the chain rule

Q: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

Q: Find the derivative of function (x+2)² (x – 1)3* f(x) -

A: f(x) = x+22x-13f'(x) = x-13×2x-2-x+223(x-1)2x-16f'(x) = x-12x+22x-1-3x+2x-14f'(x) = x+22x-2-3x-6x-14

Q: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: Find the derivative of [(xt1)*] /x.

A:

Q: Find the derivative of f(x)= xtan(x)

A:

Q: 1 Find the function whose derivative is (x+1)-

A:

Q: Determine the derivative of the given function by using two different methods 2- 3) y = ² + 3

A: Given: y=x2-3x2+34

Q: Find the derivative of the following functions and simply it whenever possible. 3. y =…

A: This is a problem related to derivative of the function. Based on the general formula of the…

Q: (3x+4` x² +5, y = tan

A: We know that d(tanx)dx = sec2(x) Now we will apply chain rule , Here we have    y = tan3x+4x2 +…

Q: Find the derivative of f(x)= (x^2)sinx

A:

Q: Find the 4th derivative of the function y=exsinx.

A:

Q: y=x²

A: I have stated the used formula in the solution

Q: Solve the derivative of f(x)=−1/√2 x +2x

A: Given- fx=-12x+2x To find- The derivative of the above function. Formula used- Using the power rule…

Q: Find the derivative of the function two ways: by simplifying the function first and by using the…

A:

Q: find the derivative of the function f(x)=x^3+2x at -3

A: find the derivative of the function f(x)

Q: Find the derivative of y = arctan² (x³)

A: This is a problem of differentiation of the function. Based on general formula we will solve this…

Q: What rule should be used in getting the derivative of y=(1−x^2 )^6

A: What rule should be used in getting the derivative of y=(1−x^2 )^6

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

A:

Q: Determine the derivative of the given function by using two different methods

A: Given,         y=x2-3x2+34

Q: Find the first derivative of f (x) = 2* 2*

A:

Q: Find the derivative of the function. f(x) = 4 3√x + 2cos x

A: The given function is ; f(x)=4/3sqrt(x) +2Cosx.

Q: Help to find the derivative of f(x)=1/3x.

A: The given function is fx=13x

Q: What is the derivative of:  ex / x2

A: The given function is: fx=exx2   As we know that; The Power law: ddxxn=nxn-1 The Quotient rule:…

Q: find the derivative by using the definition of a deriviative.f(x)= 1/3x+2

A: according to definition of derivative we will evaluate the derivative of f(x)

Q: What is the derivative of (x^2+1)^x?

A: Use the lograthim to find the derivative of given expression.

Q: Find the equation of the line tangent to the graph of the function f(x)=x-2x^2 at x=1 use the…

A: The equation of the curve is: f(x)=x-2x2

Q: 2. Find the derivative of y = (5x³ + 2 x)tanx. %3D

A:

Q: Find the derivative of the function without using the Quotient Rule. y = -

A:

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: What is the derivative of the function  x^8(ln(x))?

A: To find the derivative of the function x8(ln(x)) as follows.Redefine the function as follows.

Q: 2) Find the derivative of the function f(x) = 3x² by definition

A:

Q: Find the derivative of f(x)= 11x^2 at x=1 please use definition of derivative formula

A: Given :   y = 11x2    at x =1

Q: 9) Find the value of the derivative at the point x=2 if f (x) = xv2x – 7

A:

Q: By using the definition of the derivative, find the slope of the tangent line to the curve y = 4x −…

A:

Q: function

A:

Q: 2 Use the definition of derivative to find the equation of line tangent to f(x) = 2 through x = 3.

A: