Question

Derive y=(log2 X)³ ?

Answer 1

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Derivada da função composta ( regra da cadeia)

$\huge\boxed{\boxed{\boxed{\boxed{\sf[f(g(x))]'=f'[g(x)]\cdot g'(x)}}}}$

Derivada da potência

$\huge\boxed{\boxed{\boxed{\boxed{\sf\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}}}}}$

Derivada do logaritmo de base qualquer

$\huge\boxed{\boxed{\boxed{\boxed{\sf\dfrac{d}{dx}[\ell og_a(x)]=\dfrac{1}{x\cdot \ell n(a)}}}}}$

$\huge\boxed{\begin{array}{l}\sf y=(\ell og_2x)^3\\\sf\dfrac{dy}{dx}=3\cdot(\ell og_2x)^{3-1}\cdot\dfrac{d}{dx}(\ell og_2x)\\\sf\dfrac{dy}{dx}=3\cdot(\ell og_2x)^2\cdot\dfrac{1}{x\ell n(2)}\\\huge\boxed{\boxed{\boxed{\boxed{\sf\dfrac{dy}{dx}=\dfrac{3\cdot(\ell og_2x)^2}{x\ell n(2)}}}}}\end{array}}\blue{\checkmark}$