What is the derivative of 4xsqrt(16-x^2) ?

The derivative of 4xsqrt(16-x^2) is (4(-2x^2+16))/(sqrt(16-x^2))

What is the first derivative of 4xsqrt(16-x^2) ?

The first derivative of 4xsqrt(16-x^2) is (4(-2x^2+16))/(sqrt(16-x^2))

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\frac{d}{d x} (4 x 16 - x^{2})

\frac{4 ( - 2 x ^{2} + 16 )}{16 - x ^{2}}

Solution steps

\frac{d}{d x} (4 x 16 - x^{2})

Take the constant out:

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

= 4 \frac{d}{d x} (x 16 - x^{2})

Apply the Product Rule:

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

f = x, g = 16 - x^{2}

= 4 (\frac{d x}{d x} 16 - x^{2} + \frac{d}{d x} (16 - x^{2}) x)

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

\frac{d}{d x} (16 - x^{2}) = - \frac{x}{16 - x ^{2}}

= 4 (1 \cdot 16 - x^{2} + (- \frac{x}{16 - x ^{2}}) x)

Simplify

4 (1 \cdot 16 - x^{2} + (- \frac{x}{16 - x ^{2}}) x) : \frac{4 ( - 2 x ^{2} + 16 )}{16 - x ^{2}}

= \frac{4 ( - 2 x ^{2} + 16 )}{16 - x ^{2}}

\int_{1}^{2} 2 x x^{2} + 1 d x

n = 3 \sum \infty \frac{1}{3 ^{n}}

(\frac{1}{y ^{2}} - \frac{7}{y ^{4}}) (y + 3 y^{3})

\int \frac{1}{e ^{u}} d u

\int \frac{11 x ^{2}}{( 225 + x ^{2} ) ^{2}} d x

What is the derivative of 4xsqrt(16-x^2) ?
The derivative of 4xsqrt(16-x^2) is (4(-2x^2+16))/(sqrt(16-x^2))
What is the first derivative of 4xsqrt(16-x^2) ?
The first derivative of 4xsqrt(16-x^2) is (4(-2x^2+16))/(sqrt(16-x^2))