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Find the derivatives of the functions. $e^{2x^2-x+1/x}$

Find a linear differential operator that annihilates the given function.
${\displaystyle f\left(x\right)=3x^2-x\sin 3x+x^2{e}^{-x}\cos 4x}$

Use the Binomial Theorem to expand the binomial, ${\displaystyle {(3x+y)}^3}$ and express the result in simplified form.

A ping test determines whether a client (computer, smartphone, or similar device) communicates with another device across a network. Assume that the probability of response to a test is 3/4. The test involves a large number of runs and it continues until the first response is recorded. Define the random variable X as the number of runs of the test required to terminate the experiment. Suppose that the condition of one run does not affect that of another.
a. Determine the probability distribution of X.
b. Let A be defined as the event that the experiment ends after an even number of repetitions. Evaluate P(A).

Find the limit and discuss the continuity of the function. ${\displaystyle \underset{x,y}{lim}\to (2\pi ,4)\sin \frac{x}{y}}$

Calculate the derivatives of all orders: f'(x), f''(x), f'''(x), ${\displaystyle f^4,\dots ,f^n\left(x\right),\dots ,f\left(x\right)=e^{3x-1}}$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Im

Subtract: ${\displaystyle (14x^3-5x^2+x-9)-(4x^3-3x^2-7x+1)}$

Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.
${\displaystyle (-2x-3y)(3x+2y)}$

Subtract ${\displaystyle -2x^2+3x-9}$ from ${\displaystyle 8x^2+10x-10}$

Add the given polynomials.
${\displaystyle 12a^2{b}^2-9ab}$ and ${\displaystyle 5a^2{b}^2+4ab}$

Suppose 38 manufacturing workers are selected randomly from across Switzerland and asked what their hourly wage is. What is the probability that the sample average will be between $30.00 and $31.00?

Find the values of the trigonometric functions of θ from the information given. $cot\theta =-89,cos\theta >0$

Given ${\displaystyle f\left(x\right)=4x^2-3\text{and}g\left(x\right)=6-\frac{1}{2}{x}^2}$
a. (f of g)(4)

Find the sum of the polynomial functions.
${\displaystyle P\left(x\right)=5x^4-4x+4}$
and
${\displaystyle R\left(x\right)=2x^5-3x-8}$
${\displaystyle P\left(x\right)+R\left(x\right)=?}$

Factor the following completely
${\displaystyle 2x^3+3x^3-5x+8x^{2}y+12xy-20y}$

Subtract ${\displaystyle (10t^2+13t-19)}$ from ${\displaystyle (t^2-8)}$

Sum of polynomials
${\displaystyle 7z^4-8z^3+6}$ and ${\displaystyle 4z^2+6z}$

Multiply the polynomials:
${\displaystyle {(x+4y)}^2(3x-2y)}$

One of the zeros is given for each of the following polynomials. Find the other zeros in the field of complex numbers.
${\displaystyle x^3-4x^2+6x-4.1-i}$ is a zero