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balandron [24]
2 years ago
9

Log_{7 }(5 - 3x)Find the derivative​

Mathematics
1 answer:
V125BC [204]2 years ago
6 0

Let <em>y</em> be the expression you want to differentiate:

y=\log_7(5-3x) \implies 7^y=5-3x

Now,

7^y=e^{\ln(7^y)}=e^{y\ln(7)}

Use the chain rule to differentiate both sides with respect to <em>x</em> :

\ln(7)e^{y\ln(7)}\dfrac{\mathrm dy}{\mathrm dx}=-3

Solve for d<em>y</em>/d<em>x</em> :

\ln(7)7^y\dfrac{\mathrm dy}{\mathrm dx}=-3

\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac3{\ln(7)7^y}

\dfrac{\mathrm dy}{\mathrm dx}=\boxed{-\dfrac3{\ln(7)(5-3x)}}

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5^2•3^-1•5^-3/3^4•5^-1•3^-3
puteri [66]
Assuming you want the expression to be simplified. 

We begin with the following: 

5^{2} * 3^{-1} * \frac{5^-3}{3^{4}} * 5^{-1} * 3^{-3}

Simplify the first part, 5^{2}. That is 25. Now we have this: 

25*3^{-1.5} * \frac{-3}{3^{4}} * 5^{-1} * 3^{-3} 

Next, simplify 3^{-1}, which is 1/3, and get this: 

25* 1/3 * \frac{-3}{3^{4}} * 5^{-1} * 3^{-3} 

The next part is \frac{5^-3}{3^{4}}. Simplify the denominator, 3^{4}, which is 81. Simplify the numerator, which is 1/125. Then divide 1/125 by 81, which we will keep as a fraction for simplicity's sake, but simplify it to \frac{1}{10125}. Now we have: 

25* 1/3 * \frac{1}{10125} * 5^{-1} * 3^{-3}

Now simplify 5^{-1}, which is 0.2, or 1/5. Now we have: 

25* 1/3 * \frac{1}{10125} * 0.2 * 3^{-3} 

Finally, simplify 3^{-3}. That is 1/27. We have: 

25* 1/3 * \frac{1}{10125} * 0.2 * 1/27

Lastly, multiply them all together! Now we are done, with the product of: 

\frac{1}{6075}

That certainly did take a while to type in all the LaTex, so I really hope that helped!

Note- if anything isn't working with the LaTex, just tell me and I'll fix it! (:
3 0
2 years ago
Need number 1 and 2
m_a_m_a [10]
First one is 97
2nd one is 8000
8 0
3 years ago
6+8x2=5x<br><br> A. –2<br><br> B. –1<br><br> C. 1/3<br><br> D. \(3\)
VMariaS [17]
From order of operations, we do multiply/divide first, then add/subtract. So:
(I assume that is 8 times 2, and 5 times x, solving for x)

6+8<span>⋅</span>2 = 5x
6 + 16 = 5x
22 = 5x
x = 22/5 (twenty two fifths)
3 0
3 years ago
Angles X and Y are congruent. Imported Asset and Imported Asset . Find the degree measure of angle X.
Sphinxa [80]
You can use a diffrent kind of ruler for math then you could find the answer.
8 0
2 years ago
Transformation of quadratic functions
Kitty [74]

Answer:

g(x) = a(x − h)2 + k, where a ≠ 0.

Step-by-step explanation:

The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.

6 0
2 years ago
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