What is the derivative of y=sqrt(7x^3-6x^2-8/x) ?

The derivative of y=sqrt(7x^3-6x^2-8/x) is (21x^4-12x^3+8)/(2x^{3/2)sqrt(7x^4-6x^3-8)}

What is the first derivative of y=sqrt(7x^3-6x^2-8/x) ?

The first derivative of y=sqrt(7x^3-6x^2-8/x) is (21x^4-12x^3+8)/(2x^{3/2)sqrt(7x^4-6x^3-8)}

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derivative of

y = 7 x^{3} - 6 x^{2} - \frac{8}{x}

\frac{21 x ^{4} - 12 x ^{3} + 8}{2 x ^{\frac{3}{2}} 7 x ^{4} - 6 x ^{3} - 8}

Solution steps

\frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x})

Apply the chain rule:

\frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} \frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x})

= \frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} \frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x})

\frac{d}{d x} (7 x^{3} - 6 x^{2} - \frac{8}{x}) = 21 x^{2} - 12 x + \frac{8}{x ^{2}}

= \frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} (21 x^{2} - 12 x + \frac{8}{x ^{2}})

Simplify

\frac{1}{2 7 x ^{3} - 6 x ^{2} - \frac{8}{x}} (21 x^{2} - 12 x + \frac{8}{x ^{2}}) : \frac{21 x ^{4} - 12 x ^{3} + 8}{2 x ^{\frac{3}{2}} 7 x ^{4} - 6 x ^{3} - 8}

= \frac{21 x ^{4} - 12 x ^{3} + 8}{2 x ^{\frac{3}{2}} 7 x ^{4} - 6 x ^{3} - 8}

4 y^{^{''}} - y^{^{'}} + y = 0

y^{^{''}} + 2 y^{^{'}} - y = 10

\frac{d y}{d x} = 1 - 9 y^{2}, y (- 1) = 0

x \to 0 lim (\frac{∣ sin ( x ) ∣}{x})

\frac{d}{d x} (- \frac{600}{x ^{2}} + 4)

What is the derivative of y=sqrt(7x^3-6x^2-8/x) ?
The derivative of y=sqrt(7x^3-6x^2-8/x) is (21x^4-12x^3+8)/(2x^{3/2)sqrt(7x^4-6x^3-8)}
What is the first derivative of y=sqrt(7x^3-6x^2-8/x) ?
The first derivative of y=sqrt(7x^3-6x^2-8/x) is (21x^4-12x^3+8)/(2x^{3/2)sqrt(7x^4-6x^3-8)}