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

The derivative of (x^4-3)^3(x^2+6)^5 is 12x^3(x^4-3)^2(x^2+6)^5+10x(x^2+6)^4(x^4-3)^3

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

The first derivative of (x^4-3)^3(x^2+6)^5 is 12x^3(x^4-3)^2(x^2+6)^5+10x(x^2+6)^4(x^4-3)^3

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derivative of

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

12 x^{3} (x^{4} - 3)^{2} (x^{2} + 6)^{5} + 10 x (x^{2} + 6)^{4} (x^{4} - 3)^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((x^{4} - 3)^{3}) = 12 x^{3} (x^{4} - 3)^{2}

\frac{d}{d x} ((x^{2} + 6)^{5}) = 10 x (x^{2} + 6)^{4}

= 12 x^{3} (x^{4} - 3)^{2} (x^{2} + 6)^{5} + 10 x (x^{2} + 6)^{4} (x^{4} - 3)^{3}

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

15000 e^{- 0.6 x}

x \to 2 - lim (5 x^{3} - \frac{2}{x - 2})

9

\int_{- 6}^{6} \frac{1}{v} d v

What is the derivative of (x^4-3)^3(x^2+6)^5 ?
The derivative of (x^4-3)^3(x^2+6)^5 is 12x^3(x^4-3)^2(x^2+6)^5+10x(x^2+6)^4(x^4-3)^3
What is the first derivative of (x^4-3)^3(x^2+6)^5 ?
The first derivative of (x^4-3)^3(x^2+6)^5 is 12x^3(x^4-3)^2(x^2+6)^5+10x(x^2+6)^4(x^4-3)^3