## What is the derivative of 1 X with respect to X?

The derivative of 1/x is -1/x2.

### What is the derivative of 1 by x 2?

Explanation: We will use the power rule, which states that the derivative of xn is nxn−1 . We can use the power rule once we write 1×2 as x−2 . Thus, according to the power rule, the derivative of x−2 is −2x−2−1=−2x−3=−2×3 .

#### What is the integration of 1 by X?

Answer: The integral of 1/x is log x + C.

**Is the derivative of 1 x ln X?**

Proving that the derivative of ln(x) is 1/x by using the definition of the derivative as a limit, the properties of logarithms, and the definition of 𝑒 as a limit.

**How do you calculate derivatives?**

Basically, we can compute the derivative of f(x) using the limit definition of derivatives with the following steps:

- Find f(x + h).
- Plug f(x + h), f(x), and h into the limit definition of a derivative.
- Simplify the difference quotient.
- Take the limit, as h approaches 0, of the simplified difference quotient.

## What is the derivative of y =- 9?

Since −9 is constant with respect to x , the derivative of −9 with respect to x is 0 .

### What is the differentiation of 1 x 3?

According to the given information, we get that the value of (u = 1) and (v = x³). Hence the derivative of the function 1/x³ is -3/x⁴.

#### What is the derivative of 1 √ X?

Let f(x)=1√x , then y=1uandu=x12 , since √x=x12 . This means we have to differentiate both functions and multiply them. Let’s start with y . By the power rule y’=1×u0=1 .

**How do you derive integration formulas?**

So, (– 4 – 2x) dx = dt. After substituting, (x + 2) = t, So, dx = dt….Proofs of Integration Formulas Below:

Differentiation Formulas | Integration Formulas |
---|---|

2. ddx(ax) = a | 2. ∫adx = ax + C |

3. ddx(xn)=nxn−1 | 3. ∫xndx=xn+1n+1 + C, n ≠ -1 |

4. ddx(cosx) = -sinx | 4. ∫sinxdx = -cosx + C |

5. ddx(sinx) = cosx | 5. ∫cosxdx = sinx + C |

**What is derivative of ln x?**

1/x

The derivative of ln(x) is 1/x.

## What is derivative of XY?

And thus, your answer is xy’ + y.

### What is the derivative of x³?

3×2

Hence, derivative of x3 is 3×2. Was this answer helpful?

#### What are the 5 basic integration formulas?

Basic Formula

- ∫x n = x n+1 /n+1 + C.
- ∫cos x = sin x + C.
- ∫sin x = -cos x + C.
- ∫sec 2 x = tan x + C.
- ∫cosec 2 x = -cot x + C.
- ∫sec x tan x = sec x + C.
- ∫cosec x cot x = -cosec x + C.
- ∫dx/√ 1- x 2 = sin -1 x + C.

**How do you integrate sin2x?**

Integration of Sin2x

- Integration of sin2x means finding the integral of the function sin2x.
- The formula for the integral of sin 2x dx is given by:
- We can derive the formula of integral of sin2x using the method of integration by substitution.
- Consider ∫sin2x dx.
- Let u = 2x such that du = 2dx ⇒ dx = (½)du.

**How do you calculate derivative?**

nH*Ma*Va=nOH*Mb*Vb where: nH = number of H + ions contributed per molecule of acid, Ma = molarity of the acid, Va = volume of the acid, nOH = number of OH – ions contributed per molecule of base, Mb = molarity of base, and Vb = volume of the base. Acid base titration method Fill a burette with the solution of the titrant.

## How do you calculate higher order derivatives?

Check that the equation is linear.

### How do I find the original function given the derivative?

– Recall that – Let us define by for – Suppose that . Taking natural logarithm of both sides yields, . Hence is one to one – If then , and . Hence is onto . – Finally, for , – We have shown that is a bijective homomorphism, hence it is an isomorphism.

#### How do you solve a derivative?

power rule