derivative xsqrt(4-x^2)

Solução

derivada de

x 4 - x^{2}

\frac{- 2 x ^{2} + 4}{4 - x ^{2}}

Passos da solução

\frac{d}{d x} (x 4 - x^{2})

Aplicar a regra do produto:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 4 - x^{2}

= \frac{d x}{d x} 4 - x^{2} + \frac{d}{d x} (4 - x^{2}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (4 - x^{2}) = - \frac{x}{4 - x ^{2}}

= 1 \cdot 4 - x^{2} + (- \frac{x}{4 - x ^{2}}) x

Simplificar

1 \cdot 4 - x^{2} + (- \frac{x}{4 - x ^{2}}) x : \frac{- 2 x ^{2} + 4}{4 - x ^{2}}

= \frac{- 2 x ^{2} + 4}{4 - x ^{2}}

f (x) = (x^{2} + 3 x - 2)^{4}

f (x) = sin (2 x) cos (x), at x = π

f (x) = (x^{2} + 1)^{2}

x = - 1

x = 4