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Popular >

derivative of xsqrt(5-x^2)

Solution

derivative of

x 5 - x^{2}

Solution

\frac{- 2 x ^{2} + 5}{5 - x ^{2}}

Solution steps

\frac{d}{d x} (x 5 - x^{2})

Apply the Product Rule:

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

f = x, g = 5 - x^{2}

= \frac{d x}{d x} 5 - x^{2} + \frac{d}{d x} (5 - x^{2}) x

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

\frac{d}{d x} (5 - x^{2}) = - \frac{x}{5 - x ^{2}}

= 1 \cdot 5 - x^{2} + (- \frac{x}{5 - x ^{2}}) x

Simplify

1 \cdot 5 - x^{2} + (- \frac{x}{5 - x ^{2}}) x : \frac{- 2 x ^{2} + 5}{5 - x ^{2}}

= \frac{- 2 x ^{2} + 5}{5 - x ^{2}}

Popular Examples

f(x)=log_{8}(x)

f (x) = lo g_{8} (x)

integral of k/(x^2)

\int \frac{k}{x ^{2}} d x

y^{''}+0.1y^'+y=0

y^{^{''}} + 0.1 y^{^{'}} + y = 0

(\partial)/(\partial y)(9sqrt(x^2+y^2))

\frac{\partial}{\partial y} (9 x^{2} + y^{2})

(5x+ye^{y/x})dx-xe^{y/x}dy=0,y(1)=2

(5 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0, y (1) = 2

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(5-x^2) ?
The derivative of xsqrt(5-x^2) is (-2x^2+5)/(sqrt(5-x^2))
What is the first derivative of xsqrt(5-x^2) ?
The first derivative of xsqrt(5-x^2) is (-2x^2+5)/(sqrt(5-x^2))