What is the derivative of 2xsqrt(4-x^2) ?

The derivative of 2xsqrt(4-x^2) is (2(-2x^2+4))/(sqrt(4-x^2))

What is the first derivative of 2xsqrt(4-x^2) ?

The first derivative of 2xsqrt(4-x^2) is (2(-2x^2+4))/(sqrt(4-x^2))

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

= 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}}

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

Simplify

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

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

\frac{d}{d x} (ln (e^{x} - e^{a}))

\frac{d}{d x} (e^{x^{2} + 9 x})

\int sec^{3} (x) tan^{5} (x) d x

\int 2 x^{3} d x

\int - \frac{1}{2} \cdot sin (2 x) + \frac{1}{4} \cdot 2 x d x

What is the derivative of 2xsqrt(4-x^2) ?
The derivative of 2xsqrt(4-x^2) is (2(-2x^2+4))/(sqrt(4-x^2))
What is the first derivative of 2xsqrt(4-x^2) ?
The first derivative of 2xsqrt(4-x^2) is (2(-2x^2+4))/(sqrt(4-x^2))