What is the derivative of (6x^2+11)^{1/2} ?

The derivative of (6x^2+11)^{1/2} is (6x)/((6x^2+11)^{1/2)}

What is the first derivative of (6x^2+11)^{1/2} ?

The first derivative of (6x^2+11)^{1/2} is (6x)/((6x^2+11)^{1/2)}

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derivative of

(6 x^{2} + 11)^{\frac{1}{2}}

\frac{6 x}{( 6 x ^{2} + 11 ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((6 x^{2} + 11)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 6 x ^{2} + 11 ) ^{\frac{1}{2}}} \frac{d}{d x} (6 x^{2} + 11)

= \frac{1}{2 ( 6 x ^{2} + 11 ) ^{\frac{1}{2}}} \frac{d}{d x} (6 x^{2} + 11)

\frac{d}{d x} (6 x^{2} + 11) = 12 x

= \frac{1}{2 ( 6 x ^{2} + 11 ) ^{\frac{1}{2}}} \cdot 12 x

Simplify

\frac{1}{2 ( 6 x ^{2} + 11 ) ^{\frac{1}{2}}} \cdot 12 x : \frac{6 x}{( 6 x ^{2} + 11 ) ^{\frac{1}{2}}}

= \frac{6 x}{( 6 x ^{2} + 11 ) ^{\frac{1}{2}}}

What is the derivative of (6x^2+11)^{1/2} ?
The derivative of (6x^2+11)^{1/2} is (6x)/((6x^2+11)^{1/2)}
What is the first derivative of (6x^2+11)^{1/2} ?
The first derivative of (6x^2+11)^{1/2} is (6x)/((6x^2+11)^{1/2)}