Question

Sa se calculeze f prim
f(x)= 2 la puterea x la 2-6x

Answer 1

f(x) = 2ˣ² - 6x

f'(x) = ( 2ˣ² )' - ( 6x )' = 2ˣ²ln2 · ( x² )' - 6 = 2ˣ²ln2 · 2x - 6

f'(x) = 2x · 2ˣ²ln2 - 6

( aˣ )' = aˣln a  ( derivata elementara )

( aⁿ ) = aⁿln a · n'  ( derivata compusa )

Answer 2

$f(x) = 2^{x^{2-6x}}\\ \\ f'(x) = (x^{2-6x})'\cdot 2^{x^{2-6x}}\cdot \ln 2\\ \\ f'(x) = (e^{\ln x^{2-6x}})'\cdot 2^{x^{2-6x}}\cdot \ln 2\\ \\ f'(x) = [e^{(2-6x)\ln x}]'\cdot 2^{x^{2-6x}}\cdot \ln 2 \\ \\ f'(x) = e^{(2-6x)\ln x}\cdot \Big(-6\ln x+ \dfrac{2-6x}{x}\Big)\cdot 2^{x^{2-6x}}\cdot \ln 2\\ \\\boxed{f'(x) = x^{2-6x}\cdot \Big(\dfrac{2-6x}{x}-6\ln x\Big)\cdot 2^{x^{6-2x}}\cdot \ln 2}$