All categories

2 years ago

Find the derivative using the first principles.

Mathematics

1 answer:

lubasha [3.4K]2 years ago

3 0

$~~~~\dfrac{d}{dx} \left( \sqrt[5]{1+x} \right)\\\\\\=\dfrac{d}{dx} (1+x)^{\tfrac 15}\\\\\\=\dfrac 15 \left(1 + x\right)^{\tfrac 15 -1} \cdot \dfrac{d}{dx}(1+x)\\\\\\=\dfrac 15 (1+x)^{-\tfrac 45} \cdot(0+1)\\\\\\=\dfrac{1}{5(1+x)^{\tfrac 45}}$

You might be interested in

What does the factor is 3 that both 3x and 18 have in common.

Arlecino [84]

3 goes into both 3x and 18

4 0

3 years ago

What is the addititve inverse of 63

denis23 [38]

Additive Inverse of 63 = -63
Since the additive inverse of 63 is -63, additive inverse is also known as the opposite number.

3 0

3 years ago

Read 2 more answers

6 1/2+n=12. please explain for me I dunno how to do this.

Temka [501]

Hey there!

Let's first define our goal. Our goal here is to be able to isolate the variable, n, and solve for it by moving everything to the other side. We see that we have two sides of the equation, and by using the property of equality which states that whatever you do to one side you do to the other and the expression remains equal, we can solve this equation.

It looks like the only thing we have on the left side with n is that 6 1/2. In order to get rid of it, we must subtract it from both sides, because the property of equality states you must do the inverse operation.

We have:

n = 12 - 6 1/2

n = 5 1/2

Hope this helps!

7 0

3 years ago

Jenny studied the characteristics of two species of bacteria. The number of bacteria of species A, A(t), after t hours is repres

fredd [130]

Answer: D . $N(t) = 3 + (0.25t)^3 - 8(1.06)^t$

Step-by-step explanation:

Given : Jenny studied the characteristics of two species of bacteria. The number of bacteria of species A, A(t), after t hours is represented by the function,

$A(t) = 5 + (0.25t)^3$

The number of bacteria of species B, B(t), after t hours is represented by the function, $B(t) = 2 + 8(1.06)^t$

Then, the difference in the number of bacteria, N(t), of both the species after t hours will be :-

$N(t)=A(t)-B(t)\\\\=5 + (0.25t)^3-(2 + 8(1.06)^t)\\\\=5 + (0.25t)^3-2-8(1.06)^t\\\\=5-2 +(0.25t)^3-8(1.06)^t\\\\=3+(0.25t)^3-8(1.06)^t$

Hence, the correct answer should be : D . $N(t) = 3 + (0.25t)^3 - 8(1.06)^t$

7 0

3 years ago

1862 divided by 17383

Kipish [7]

Answer:

do i round to the nearest hundredth?if so it would be 0.11

Step-by-step explanation:

6 0

3 years ago

Find the derivative using the first principles. ​

Find the derivative using the first principles.