What is the derivative of (t^4-1)^9(t^3+1)^8 ?

The derivative of (t^4-1)^9(t^3+1)^8 is 36t^3(t^4-1)^8(t^3+1)^8+24t^2(t^3+1)^7(t^4-1)^9

What is the first derivative of (t^4-1)^9(t^3+1)^8 ?

The first derivative of (t^4-1)^9(t^3+1)^8 is 36t^3(t^4-1)^8(t^3+1)^8+24t^2(t^3+1)^7(t^4-1)^9

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derivative of

(t^{4} - 1)^{9} (t^{3} + 1)^{8}

36 t^{3} (t^{4} - 1)^{8} (t^{3} + 1)^{8} + 24 t^{2} (t^{3} + 1)^{7} (t^{4} - 1)^{9}

Solution steps

\frac{d}{d t} ((t^{4} - 1)^{9} (t^{3} + 1)^{8})

Apply the Product Rule:

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

f = (t^{4} - 1)^{9}, g = (t^{3} + 1)^{8}

= \frac{d}{d t} ((t^{4} - 1)^{9}) (t^{3} + 1)^{8} + \frac{d}{d t} ((t^{3} + 1)^{8}) (t^{4} - 1)^{9}

\frac{d}{d t} ((t^{4} - 1)^{9}) = 36 t^{3} (t^{4} - 1)^{8}

\frac{d}{d t} ((t^{3} + 1)^{8}) = 24 t^{2} (t^{3} + 1)^{7}

= 36 t^{3} (t^{4} - 1)^{8} (t^{3} + 1)^{8} + 24 t^{2} (t^{3} + 1)^{7} (t^{4} - 1)^{9}

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

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

\frac{x}{x + 1}

\int + \frac{4 y}{1} d y

x \to 2 lim (\frac{1}{( x + 2 )})

What is the derivative of (t^4-1)^9(t^3+1)^8 ?
The derivative of (t^4-1)^9(t^3+1)^8 is 36t^3(t^4-1)^8(t^3+1)^8+24t^2(t^3+1)^7(t^4-1)^9
What is the first derivative of (t^4-1)^9(t^3+1)^8 ?
The first derivative of (t^4-1)^9(t^3+1)^8 is 36t^3(t^4-1)^8(t^3+1)^8+24t^2(t^3+1)^7(t^4-1)^9