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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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