Consider the function $y(x) = 2^{5x^2+3}$. Is this a composite function? If so, how can you choose $v(x)$ and $u(v)$ in a convenient way?
Antwoord 1 correct
Correct
Antwoord 2 optie
$y(x)$ is a composite function consisting of $v(x) = x^2$ and $u(v) = 2^{5v+3}$.
Antwoord 2 correct
Fout
Antwoord 3 optie
$y(x)$ is a composite function consisting of $v(x) = 5x^2$ and $u(v) = 2^{v+3}$.
Antwoord 3 correct
Fout
Antwoord 4 optie
$y(x)$ is not a compostite function, because $y(x)$ cannot be written as $u(v(x))$.
Antwoord 4 correct
Fout
Antwoord 1 optie
$y(x)$ is a composite function consisting of $v(x) = 5x^2+3$ and $u(v) = 2^v$.
Antwoord 1 feedback
Correct: It holds that
$$u(v(x)) = 2^{v(x)} = 2^{5x^2+3} = y(x)$$
and moreover, $v(x)$ and $u(v)$ can be differentiated by the use of Derivatives elementary functions and the Rules of differentiation.
Go on.
$$u(v(x)) = 2^{v(x)} = 2^{5x^2+3} = y(x)$$
and moreover, $v(x)$ and $u(v)$ can be differentiated by the use of Derivatives elementary functions and the Rules of differentiation.
Go on.
Antwoord 2 feedback
Wrong: $y(x)$ is indeed a composite function and $y(x) = u(v(x))$, but $u(v)$ cannot be differentiated by the use of Derivatives elementary functions and the Rules of differentiation.
See Composite function.
See Composite function.
Antwoord 3 feedback
Wrong: $y(x)$ is indeed a composite function and $y(x) = u(v(x))$, but $u(v)$ cannot be differentiated by the use of Derivatives elementary functions and the Rules of differentiation.
See Composite function.
See Composite function.
Antwoord 4 feedback
Wrong: $y(x)$ is a composite function. (Every function can be written as $u(v(x))$.)
See Composite function.
See Composite function.