What is the derivative of x^7(x^2-3/(x^3)) ?

The derivative of x^7(x^2-3/(x^3)) is 9x^8-12x^3

What is the first derivative of x^7(x^2-3/(x^3)) ?

The first derivative of x^7(x^2-3/(x^3)) is 9x^8-12x^3

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derivative of

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

9 x^{8} - 12 x^{3}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{7}, g = x^{2} - \frac{3}{x ^{3}}

= \frac{d}{d x} (x^{7}) (x^{2} - \frac{3}{x ^{3}}) + \frac{d}{d x} (x^{2} - \frac{3}{x ^{3}}) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

\frac{d}{d x} (x^{2} - \frac{3}{x ^{3}}) = 2 x + \frac{9}{x ^{4}}

= 7 x^{6} (x^{2} - \frac{3}{x ^{3}}) + (2 x + \frac{9}{x ^{4}}) x^{7}

Simplify

7 x^{6} (x^{2} - \frac{3}{x ^{3}}) + (2 x + \frac{9}{x ^{4}}) x^{7} : 9 x^{8} - 12 x^{3}

= 9 x^{8} - 12 x^{3}

n = 0 \sum \infty \frac{1}{n \cdot 2 ^{n}}

k = 0 \sum \infty \frac{1}{k ^{2} + 1}

2 x y d x = (1 + y) d y

\frac{\partial}{\partial y} (x^{3} - 3 x y^{2} + y^{3})

f (x) = \frac{2 t + 3}{t + 5}

What is the derivative of x^7(x^2-3/(x^3)) ?
The derivative of x^7(x^2-3/(x^3)) is 9x^8-12x^3
What is the first derivative of x^7(x^2-3/(x^3)) ?
The first derivative of x^7(x^2-3/(x^3)) is 9x^8-12x^3