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3 years ago

By applying the Product Rule twice, one can prove that if f, g, and h are differentiable, then (fgh)′=f′gh+fg′h+fgh′.

Mathematics

1 answer:

Diano4ka-milaya [45]3 years ago

8 0

f(x) given to us is e^(x)

Hence,

d/dx [f(x)^3] = 3 * [e^(x)]^2 * [e^(x)]'

= 3 * e^(2x) * e^(x)

= 3e^(3x)

which is the derivative of e^(3x and this is what we are finding in the answer.

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The graph of g(x) is a transformation of the graph of f(x)=3x. Enter the equation for g(x) in the box. G(x) =.

dalvyx [7]

Function transformation involves changing the form of a function

The function g(x) is $\mathbf{g(x) = 8(2)^x}$

The function is given as:

$\mathbf{f(x) = 3^x}$

g(x) is an exponential function that passes through points (-2,2) and (-1,4).

An exponential function is represented as:

$\mathbf{y = ab^x}$

At point (-2,2), we have:

$\mathbf{2 = ab^{-2}}$

At point (-1,4), we have:

$\mathbf{4 = ab^{-1}}$

Divide both equations

$\mathbf{\frac 42=\frac{ab^{-1}}{ab^{-2}}}$

Simplify

$\mathbf{2=\frac{b^{-1}}{b^{-2}}}$

Apply law of indices

$\mathbf{2=b^{-1+2}}$

$\mathbf{2=b}$

Rewrite as:

$\mathbf{b =2}$

Substitute 2 for b in $\mathbf{2 = ab^{-2}}$

$\mathbf{2 =a(2^{-2})}$

This gives

$\mathbf{2 =a(\frac 14)}$

Multiply both sides by 4

$\mathbf{a = 8}$

Substitute 8 for (a) and 2 for (b) in $\mathbf{y = ab^x}$

$\mathbf{y = 8(2)^x}$

Express as a function

$\mathbf{g(x) = 8(2)^x}$

Hence, the function g(x) is $\mathbf{g(x) = 8(2)^x}$

Read more about exponential functions at:

brainly.com/question/11487261

8 0

3 years ago

A political candidate collected $1,749 from a fund raising dinner. If each supporter contributed at least $50, what is the great

Irina-Kira [14]

Answer: C. 34

Step-by-step explanation: 1749 divided by 50 is 34.94 however those extra cents has to just be counted like a tip because it’s not big enough to count as someone. It has to be a full number. Sorry if I explain weird!

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3 years ago

Which table contains only values that satisfy

Anna007 [38]

Answer:

Table A

$y = 1.5x + 4 \\ table \: A \: satisfies \: the \: equation$

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3 years ago

What is 7 + 6x for x = -3?

Temka [501]

Answer:

-11

Step-by-step explanation:

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3 years ago

Read 2 more answers

EXPERTS/ACe/GENIUSES <br> Ill mark as brainlist if correct

katrin2010 [14]

It's probably the first one: "People responded to Earth Day with letters..."
Since it's more of a detail that supports a fact, it's not as important as the other three.

3 0

4 years ago