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

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

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

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

Popular >

derivative of

y = x 16 - x^{2}

\frac{- 2 x ^{2} + 16}{16 - x ^{2}}

Solution steps

\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}

= \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}}

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

Simplify

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

= \frac{- 2 x ^{2} + 16}{16 - x ^{2}}

\frac{d}{d x} (ln (cos^{2} (x)))

y^{^{''}} + y = 3 x^{2}

\int_{0}^{\frac{π}{8}} cos (4 x) d x

\frac{d}{d x} (5 x^{4} - 3 x^{2} + \frac{1}{x})

x \to 4 lim (∣ x + 4 ∣)

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