What is the derivative of x^2(x^3+4)(x^5-6) ?

The derivative of x^2(x^3+4)(x^5-6) is 10x^9+28x^6-30x^4-48x

What is the first derivative of x^2(x^3+4)(x^5-6) ?

The first derivative of x^2(x^3+4)(x^5-6) is 10x^9+28x^6-30x^4-48x

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derivative of

x^{2} (x^{3} + 4) (x^{5} - 6)

10 x^{9} + 28 x^{6} - 30 x^{4} - 48 x

Solution steps

\frac{d}{d x} (x^{2} (x^{3} + 4) (x^{5} - 6))

Apply the Product Rule:

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

f = x^{2}, g = (x^{3} + 4) (x^{5} - 6)

= \frac{d}{d x} (x^{2}) (x^{3} + 4) (x^{5} - 6) + \frac{d}{d x} ((x^{3} + 4) (x^{5} - 6)) x^{2}

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

\frac{d}{d x} ((x^{3} + 4) (x^{5} - 6)) = 8 x^{7} + 20 x^{4} - 18 x^{2}

= 2 x (x^{3} + 4) (x^{5} - 6) + (8 x^{7} + 20 x^{4} - 18 x^{2}) x^{2}

Simplify

2 x (x^{3} + 4) (x^{5} - 6) + (8 x^{7} + 20 x^{4} - 18 x^{2}) x^{2} : 10 x^{9} + 28 x^{6} - 30 x^{4} - 48 x

= 10 x^{9} + 28 x^{6} - 30 x^{4} - 48 x

What is the derivative of x^2(x^3+4)(x^5-6) ?
The derivative of x^2(x^3+4)(x^5-6) is 10x^9+28x^6-30x^4-48x
What is the first derivative of x^2(x^3+4)(x^5-6) ?
The first derivative of x^2(x^3+4)(x^5-6) is 10x^9+28x^6-30x^4-48x