What is the derivative of (6x^{0.5}-x^2^2) ?

The derivative of (6x^{0.5}-x^2^2) is (2(3-2x^{3/2})(6x^{1/2}-x^2))/(x^{1/2)}

What is the first derivative of (6x^{0.5}-x^2^2) ?

The first derivative of (6x^{0.5}-x^2^2) is (2(3-2x^{3/2})(6x^{1/2}-x^2))/(x^{1/2)}

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\frac{d}{d x} ((6 x^{0.5} - x^{2})^{2})

\frac{2 ( 3 - 2 x ^{\frac{3}{2}} ) ( 6 x ^{\frac{1}{2}} - x ^{2} )}{x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((6 x^{0.5} - x^{2})^{2})

Apply the chain rule:

2 (6 x^{0.5} - x^{2}) \frac{d}{d x} (6 x^{0.5} - x^{2})

= 2 (6 x^{0.5} - x^{2}) \frac{d}{d x} (6 x^{0.5} - x^{2})

\frac{d}{d x} (6 x^{0.5} - x^{2}) = \frac{3 - 2 x ^{\frac{3}{2}}}{x ^{\frac{1}{2}}}

= 2 (6 x^{0.5} - x^{2}) \frac{3 - 2 x ^{\frac{3}{2}}}{x ^{\frac{1}{2}}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 ( 3 - 2 x ^{\frac{3}{2}} ) ( 6 x ^{\frac{1}{2}} - x ^{2} )}{x ^{\frac{1}{2}}}

\int_{1}^{3} (\frac{x}{x ^{2} + 1}) d x

2 - lo g_{10} (a)

\int \frac{12 x ^{2}}{2 x + 1} d x

x \to 0 lim (\frac{4 x ^{2} - 2 x}{x})

\frac{\partial}{\partial x} (ln (x^{2} + 3 y^{2} + 8))

What is the derivative of (6x^{0.5}-x^2^2) ?
The derivative of (6x^{0.5}-x^2^2) is (2(3-2x^{3/2})(6x^{1/2}-x^2))/(x^{1/2)}
What is the first derivative of (6x^{0.5}-x^2^2) ?
The first derivative of (6x^{0.5}-x^2^2) is (2(3-2x^{3/2})(6x^{1/2}-x^2))/(x^{1/2)}