What is the derivative of \sqrt[4]{6x^4-7x^2} ?

The derivative of \sqrt[4]{6x^4-7x^2} is (x(12x^2-7))/(2(6x^4-7x^2)^{3/4)}

What is the first derivative of \sqrt[4]{6x^4-7x^2} ?

The first derivative of \sqrt[4]{6x^4-7x^2} is (x(12x^2-7))/(2(6x^4-7x^2)^{3/4)}

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العربية

\frac{x ( 12 x ^{2} - 7 )}{2 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}}

Solution steps

Apply the chain rule:

\frac{1}{4 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (6 x^{4} - 7 x^{2})

= \frac{1}{4 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (6 x^{4} - 7 x^{2})

\frac{d}{d x} (6 x^{4} - 7 x^{2}) = 24 x^{3} - 14 x

= \frac{1}{4 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}} (24 x^{3} - 14 x)

Simplify

\frac{1}{4 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}} (24 x^{3} - 14 x) : \frac{x ( 12 x ^{2} - 7 )}{2 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}}

= \frac{x ( 12 x ^{2} - 7 )}{2 ( 6 x ^{4} - 7 x ^{2} ) ^{\frac{3}{4}}}

What is the derivative of \sqrt[4]{6x^4-7x^2} ?
The derivative of \sqrt[4]{6x^4-7x^2} is (x(12x^2-7))/(2(6x^4-7x^2)^{3/4)}
What is the first derivative of \sqrt[4]{6x^4-7x^2} ?
The first derivative of \sqrt[4]{6x^4-7x^2} is (x(12x^2-7))/(2(6x^4-7x^2)^{3/4)}