Home > Calculus > First Principles Example 3: square root of x

What is the derivative of #6 (3^(2x-1))#?

The answer following the book is #4 ln(3)3^(2x)#. I think it is wrong.
I think the answer should be #12(3^(2x-1))ln3#

Answer 1

Ezekiel Alexander

Both are same. #(dy)/(dx)=4*ln3*3^(2x)# or #12*3^(2x-1)*ln3#

For the inquirer

Actually, both are identical to

#12*3^(2x-1)*ln3#

= #4*3^1*3^(2x-1)*ln3#

= #4*3^(1+2x-1)*ln3#

= #4*ln3*3^(2x)# - observe that this answer is less complicated.

For those who might be interested in knowing

As #y=6*3^(2x-1)=2*3*3^(2x-1)=2*3^(1+2x-1)=2*3^(2x)#

Now taking log on both side (base #e#), we get

#lny=ln2+2xln3#

and differentiating #1/y*(dy)/(dx)=2*ln3#

or #(dy)/(dx)=2*ln3*y#

= #2*ln3*(2*3^(2x))#

= #4*ln3*3^(2x)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emily Ammerman

The response provided by the book and yours are identical. I will demonstrate this by beginning with your response:

#12(3^(2x-1))ln(3)#

Because addition (or subtraction) of exponents is equal to the multiplication of the base with the two exponents, I can separate #3^(2x-1)# into #3^(2x)3^-1#:

#12(3^(2x))(3^-1)ln(3)#

Because a negative exponent is the same as division, I can write #3^-1# as #1/3#:

#12(3^(2x))1/3ln(3)#

We finish by observing that #12/3 = 4#:

#4(3^(2x))ln(3)#

This matches the response provided in the book.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 3

Isabella Ackerman

The derivative of ( 6 \cdot 3^{2x-1} ) with respect to ( x ) is ( 36 \cdot 3^{2x-1} \cdot \ln(3) ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

What is the derivative of #6 (3^(2x-1))#?

The answer following the book is #4 ln(3)3^(2x)#. I think it is wrong. I think the answer should be #12(3^(2x-1))ln3#

The answer following the book is #4 ln(3)3^(2x)#. I think it is wrong.
I think the answer should be #12(3^(2x-1))ln3#