What is the derivative of-(6x^2-6/(sqrt(x^3-3x+2))) ?

The derivative of-(6x^2-6/(sqrt(x^3-3x+2))) is -(3(x+3))/((x+2)sqrt(x+2))

What is the first derivative of-(6x^2-6/(sqrt(x^3-3x+2))) ?

The first derivative of-(6x^2-6/(sqrt(x^3-3x+2))) is -(3(x+3))/((x+2)sqrt(x+2))

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

- \frac{3 ( x + 3 )}{( x + 2 ) x + 2}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

= - \frac{3 ( x + 3 )}{( x + 2 ) x + 2}

\int (5 + 9 x)^{8} (9) d x

\int \frac{cos ^{3} ( x )}{sin ( x )} d x

\int \frac{2 x + 4}{x ^{2} + 5 x - 6} d x

y = x^{3} - 7 x, y = - 4 x + 2

x \to 2 lim ((x + 4)^{2})

What is the derivative of-(6x^2-6/(sqrt(x^3-3x+2))) ?
The derivative of-(6x^2-6/(sqrt(x^3-3x+2))) is -(3(x+3))/((x+2)sqrt(x+2))
What is the first derivative of-(6x^2-6/(sqrt(x^3-3x+2))) ?
The first derivative of-(6x^2-6/(sqrt(x^3-3x+2))) is -(3(x+3))/((x+2)sqrt(x+2))