Find the derivative of the function. y = sin−1(6x + 1)

1 answer:

7 0

If you don't know the derivative of the inverse of sine, you can use implicit differentiation. Apply sine to both sides:

$y=\sin^{-1}(6x+1)\implies\sin y=6x+1$

(true for <em>y</em> between -π/2 and π/2)

Now take the derivative of both sides and solve for it:

$\cos y\dfrac{\mathrm dy}{\mathrm dx}=6$

$\dfrac{\mathrm dy}{\mathrm dx}=6\sec y$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\cos\left(\sin^{-1}(6x+1)\right)}$

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac6{\sqrt{1-(6x+1)^2}}$

You might be interested in

Graph the solution if the this inequality 4/9x-10>x/3-12

cupoosta [38]

You want to isolate the x-term from the constant term, so you can subtract x/3 and add 10. This gives you

... 4/9x -10 -x/3 +10 > x/3 -12 -x/3 +10

... 1/9x > -2 . . . . . . collect terms

Now, you can multiply by 9 to see the condition on x.

... 9(1/9x) > -2(9)

... x > -18

On the x-y plane, the graph of this will be a dashed line at x=-18, and the half-plane to the right of that line will be shaded.

On a number line, there will be an open circle at x=-18, and the number line to the right of that circle will be marked (bold, colored, shaded, whatever).

4 0

3 years ago

Identify the type of function represented by... please help

Vladimir [108]

Answer:

Exponential decay.

Step-by-step explanation:

You can use a graphing utility to check this pretty quickly, but you can also look at the equation and get the answer. Since the function has a variable in the exponent, it definitely won't be a linear equation. Quadratic equations are ones of the form ax^2 + bx + c, and your function doesn't look like that, so already you've ruled out two answers.

From the start, since we have a variable in the exponent, we can recognize that it's exponential. Figuring out growth or decay is a little more complicated. Having a negative sign out front can flip the graph; having a negative sign in the exponent flips the graph, too. In your case, you have no negatives; just 2(1/2)^x. What you need to note here, and you could use a few test points to check, is that as x gets bigger, (1/2) will get smaller and smaller. Think about it. When x = 0, 2(1/2)^0 simplifies to just 2. When x = 1, 2(1/2)^1 simplifies to 1. Already, we can tell that this graph is declining, but if you want to make sure, try a really big value for x, like 100. 2(1/2)^100 is a value very very very veeery close to 0. Therefore, you can tell that as the exponent gets larger, the value of the function goes down and gets closer and closer to zero. This means that it can't be exponential growth. In the case of exponential growth, as the exponent gets bigger, your output should increase, too.

3 0

3 years ago

Find hcf and LCM of 40 ,60 and 80

andre [41]

hear here is your answer in attachment attach