Question

okay i need to find the derivative of

f(x)=cosπ(x^2)

and if you could show steps it would be GREATLY appreciated. thank you so much!

Answer 1

Go on :

calc101 dot com

When page be open click option :

derivatives

When page be open type your function and clik option :

DO IT

You will see solution step-by-step

Remark :

If expresion for f(x) mean :

cos pi* ( x ^ 2 )

type :

cos[pi]*x^2

If expresion for f(x) mean :

cos ( pi * x ^ 2 )

type :

cos[pi*x^2]

Answer 2

I read that as

y = cos (πx^2)

dy/dx = - sin(πx^2) (2πx)
= -2πx sin(πx^2)

Answer 3

[AI-generated answer — Explain Bot]

To find the derivative of the function f(x) = cos(πx^2), you can use the chain rule. The chain rule states that if you have a composition of functions, you can find the derivative by taking the derivative of the outer function, multiplied by the derivative of the inner function.

Let's break down the function f(x) into its composite functions:
- The outer function is cos(u), where u = πx^2
- The inner function is u = πx^2

Now, we can find the derivative step by step.

Step 1: Find the derivative of the outer function
The derivative of cos(u) is -sin(u). In our case, u = πx^2, so the derivative of cos(πx^2) is -sin(πx^2).

Step 2: Find the derivative of the inner function
The derivative of u = πx^2 can be found by applying the power rule for differentiation. Since the power is 2, we multiply the coefficient π by the power and subtract 1 from the power. So, the derivative of πx^2 is (2πx).

Step 3: Apply the chain rule
Now, we take the derivative of the outer function (-sin(πx^2)) and multiply it by the derivative of the inner function (2πx).

Therefore, the derivative of f(x) = cos(πx^2) is:
f'(x) = -sin(πx^2) * (2πx)

Simplifying further, we can write it as:
f'(x) = -2πx * sin(πx^2)

And that's how you find the derivative of f(x) = cos(πx^2) using the chain rule!