What is the derivative of f(x)=sqrt(5x^6-12) ?

The derivative of f(x)=sqrt(5x^6-12) is (15x^5)/(sqrt(5x^6-12))

What is the first derivative of f(x)=sqrt(5x^6-12) ?

The first derivative of f(x)=sqrt(5x^6-12) is (15x^5)/(sqrt(5x^6-12))

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derivative

\frac{15 x ^{5}}{5 x ^{6} - 12}

Solution steps

\frac{d}{d x} (5 x^{6} - 12)

Apply the chain rule:

\frac{1}{2 5 x ^{6} - 12} \frac{d}{d x} (5 x^{6} - 12)

= \frac{1}{2 5 x ^{6} - 12} \frac{d}{d x} (5 x^{6} - 12)

\frac{d}{d x} (5 x^{6} - 12) = 30 x^{5}

= \frac{1}{2 5 x ^{6} - 12} \cdot 30 x^{5}

Simplify

\frac{1}{2 5 x ^{6} - 12} \cdot 30 x^{5} : \frac{15 x ^{5}}{5 x ^{6} - 12}

= \frac{15 x ^{5}}{5 x ^{6} - 12}

What is the derivative of f(x)=sqrt(5x^6-12) ?
The derivative of f(x)=sqrt(5x^6-12) is (15x^5)/(sqrt(5x^6-12))
What is the first derivative of f(x)=sqrt(5x^6-12) ?
The first derivative of f(x)=sqrt(5x^6-12) is (15x^5)/(sqrt(5x^6-12))