What is the derivative of (x^2-1(x^2-10x+2/(x^2))) ?

The derivative of (x^2-1(x^2-10x+2/(x^2))) is 4x^3-30x^2-2x+4/(x^3)+10

What is the first derivative of (x^2-1(x^2-10x+2/(x^2))) ?

The first derivative of (x^2-1(x^2-10x+2/(x^2))) is 4x^3-30x^2-2x+4/(x^3)+10

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\frac{d}{d x} ((x^{2} - 1) (x^{2} - 10 x + \frac{2}{x ^{2}}))

4 x^{3} - 30 x^{2} - 2 x + \frac{4}{x ^{3}} + 10

Solution steps

\frac{d}{d x} ((x^{2} - 1) (x^{2} - 10 x + \frac{2}{x ^{2}}))

Simplify

(x^{2} - 1) (x^{2} - 10 x + \frac{2}{x ^{2}}) : x^{4} - 10 x^{3} + 2 - x^{2} + 10 x - \frac{2}{x ^{2}}

= \frac{d}{d x} (x^{4} - 10 x^{3} + 2 - x^{2} + 10 x - \frac{2}{x ^{2}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{4}) - \frac{d}{d x} (10 x^{3}) + \frac{d}{d x} (2) - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (10 x) - \frac{d}{d x} (\frac{2}{x ^{2}})

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (10 x^{3}) = 30 x^{2}

\frac{d}{d x} (2) = 0

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (10 x) = 10

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

= 4 x^{3} - 30 x^{2} + 0 - 2 x + 10 - (- \frac{4}{x ^{3}})

Simplify

= 4 x^{3} - 30 x^{2} - 2 x + \frac{4}{x ^{3}} + 10

\int (ln (x))^{5} d x

t^{3} \frac{d y}{d t} + 3 t^{2} y = 8 cos (t), y (π) = 0

y = (x^{2} - 2 x + 2) e^{\frac{5 x}{2}}

\int sec (θ) tan (θ) d θ

\frac{d}{d t} (p (t) e^{t})

What is the derivative of (x^2-1(x^2-10x+2/(x^2))) ?
The derivative of (x^2-1(x^2-10x+2/(x^2))) is 4x^3-30x^2-2x+4/(x^3)+10
What is the first derivative of (x^2-1(x^2-10x+2/(x^2))) ?
The first derivative of (x^2-1(x^2-10x+2/(x^2))) is 4x^3-30x^2-2x+4/(x^3)+10