Question

A derivada de ( 5x² + 7x - 2 ) é :

Answer 1

$\dfrac{d}{dx}[a(x)\pm b(x)\pm c(x)\pm...\pm z(x)]=a'(x)\pm b'(x)\pm c'(x)\pm...\pm z'(x)\\\\\\\dfrac{d}{dx}x^{n}=n\cdot x^{n-1}\\\\\\\dfrac{d}{dx}kf(x)=k\dfrac{d}{dx}f(x)=kf'(x)\\\\\\\dfrac{d}{dx}k=0$

* k é uma constante real
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$f(x)=5x^{2}+7x-2\\\\f'(x)=\frac{d}{dx}5x^{2}+\frac{d}{dx}7x-\frac{d}{dx}2\\\\f'(x)=5\frac{d}{dx}x^{2}+7\frac{d}{dx}x-0\\\\f'(x)=5\cdot2\cdot x^{2-1}+7\cdot1\cdot x^{1-1}\\\\f'(x)=10x^{1}+7x^{0}\\\\\boxed{\boxed{f'(x)=10x+7}}$