Differentiate (лx)^e?

Question

that's 'pi' by the way

Answer 1

First look at an easier example:
f(x) = 3x^2
f'(x) = 6x

pi is a constant, so:
f(x) = pi*x^e
f'(x) = e*pi*x^(e-1)

You can check the answer by integrating.

G

Answer 2

f(x) = [(pi)(x)]^e

The first thing we need to do is bring each of those inside terms to the power of e. After all, (ab)^n = a^n b^n

f(x) = (pi^e)(x^e)

Note that pi to the power of e is simply a constant. For that reason, when we take the derivative, we ignore it and take the derivative of the rest.

f'(x) = (pi^e) (ex^(e - 1))

Cleaning this up a bit,

f'(x) = e * pi^e * x^(e - 1)

Answer 3

(e(pi^2)x)^(e-1)

We would use the chain rule in this circumstance. u=(pi)x
u^e=eu^(e-1). Substitute u and multiply by du/dx.

(pi)x^e=(e(pi^2)x)^(e-1)

I hope that this helps.

Answer 4

y=(pi x)^e

y'=e(pi x)^(e-1) * pi

by general power rule

Answer 5

Differentiate (πx)^e with respect to x. π and e are just contants so:

(πx)^e = (π^e)(x^e)

d{(π^e)(x^e)}/dx = e(π^e)x^(e-1)

Answer 6

d/dx[pi*x]^e = (pi^e)d/dx[x^e]
d/dx[x^e] = e*x^(e-1)
so d/dx[pi*x]^e = (pi^e)(e)x^(e-1)

Answer 7

y=(лx)^e
y'=e*л^e * x^(e-1)

Answer 8

y = (лx)^e = (π^e)(x^e)
y' = e(π^e)x^(e - 1) = (e(лx)^e)/x