the derivative of e^2x is itself, e^2x and then this is multiplied by 2.
so that part is 2e^2x
and the derivative of any non ln logarithm is 1/ln of the base which gives me 1/ln3
maybe the answer should be 2e^2x/ln3 ?
Homework Statement
y = log base 3 e^2x
Homework Equations
The Attempt at a Solution
I got y' = 2e^2x divided by e^2xln3
is this right?
Sorry for the pathetic way of presenting this. I haven't been able to use the lancet program for proper ways to write mathematical stuff
Homework Statement
y = 5ln(7lnx)
Homework Equations
y' = 5 x 1/7lnx +97lnx0 x 1/x
= 5(7lnx)/7lnx + 5ln x 7/x
The Attempt at a Solution
y' = 5 + 35ln/x
is this right?
Homework Statement
A 10' ladderis leaning against a house when its base starts to slide away
By the time the base is 6' fromthe house, the base is moving away at a rate of 16 ft/sec
a)What is the rate of change of the height of the top of the ladder?
b)At what rate is the area of...
Homework Statement
The function V(x) = x(14-2x)(15-x) 0<x<7 models the volume of a box
Find the extreme values of V
and tell whether these represent the smallest and largest volumes or only the smallest or only the largest volumes
Homework Equations
The Attempt at a Solution...
Homework Statement
When a circular plate of metal is heated in an oven, its radius increases at a rate of
0.04 cm/min At what rate is the plate's area increasing when r is 54 cm
Homework Equations
The Attempt at a Solution
let r be the radius
dy/dr = 0.04 cm/min...
Homework Statement
Find the value of y = sec^-1(9s^4 + 7) with respect to s
Homework Equations
The Attempt at a Solution
secy = 9s^4 + 7
but where do I go from here?
Homework Statement
y = 2x^2pi Give an exact answer in terms of pi
Homework Equations
The Attempt at a Solution
y' = 4pix^pi
Is this as far as I can go with this?
Homework Statement
y = secx
find the equation of the tangent to the curve at x = -9pi/4 and -7pi/4
Homework Equations
the derivative is secxtanx. do I just subsitute in the values -9pi/4 and then -7pi/4 to get the answer to the slope then what?
The Attempt at a Solution
Homework Statement
Given 5y^2 = 4x - 3/4x + 3
Homework Equations
is it permissable to say this is equal to y^2 = 4x -3 /5(4x + 3) and then 2y(dy)/(dx) = what the right side equals thru using the quotient rule?
I know the answer is dy/dx = 12/5y(4x + 3)^2 but I don't know how to...