Logarithmic differentiation means tAke logarithm of both sides to make the function easier to find the derivative.
y = (sinx)^lnx
ln(y) = ln((sinx)^lnx)
power rule logarithm
ln(y) = ln(x) ln(sinx)
Take derivative
y'/y = ln(sinx)(1/x) + ln(x) cosx/sinx
multiply both sides by y
y' = y( ln(sinx)/x + ln(x)cotx )
remember y = (sinx)^lnx
sub this in for y
y' = (ln(sinx)/x + ln(x)cotx)(sinx)^lnx
Hello :
<span>f(x)=x²+4x-5
</span><span>The axis of symmetry for a function in the form f(x)=x^2+4x-5 is x=-2 :
</span>f(x) = (x+2)² + b
f(x) x²+4x+4+b= x² +4x-5
4+b= -5
b = -9
the vertex is : (2 , -9)
<u>answer (in words)</u>
FALSE. the coordinate pair (5, 2) is not a solution to the equation 
. in order to figure out whether or not the statement is true or false, plug the 
and 
values from the coordinate pair (5, 2) into the given equation, . if both sides of the equation end up equal, the coordinate pair is a solution to the equation. if not, the coordinate pair is not a solution to that equation.
<em>(i hope i explained that well enough, i'm better at explaining it algebraically as opposed to putting it into words lol)</em>
<u>answer (algebraic/steps for solving)</u>
first, plug in 5 for in the equation .
- ⇒
then plug in 2 for .
- ⇒
now your equation is . all that's left to do is to simplify. you can do this in whatever order you'd like, but i'll start with multiplying 2 · 5.
- ⇒
multiply 3 · 2.
- ⇒
add 10 + 6.
- ⇒
16 and 10 are <em>not</em> equal, therefore (5, 2) is not a solution to the equation . in order for a coordinate pair to be the solution to an equation, both sides of the equation need to end up equal after solving and simplifying.
i hope this helps! have a great rest of your day <3
Answer:
The order is (-10,-1,0,1,10)
