What is the derivative of (x^2+9)^2(x-9) ?

The derivative of (x^2+9)^2(x-9) is 5x^4-36x^3+54x^2-324x+81

What is the first derivative of (x^2+9)^2(x-9) ?

The first derivative of (x^2+9)^2(x-9) is 5x^4-36x^3+54x^2-324x+81

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derivative of

(x^{2} + 9)^{2} (x - 9)

5 x^{4} - 36 x^{3} + 54 x^{2} - 324 x + 81

Solution steps

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

Apply the Product Rule:

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

f = (x^{2} + 9)^{2}, g = x - 9

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

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

\frac{d}{d x} (x - 9) = 1

= 4 x (x^{2} + 9) (x - 9) + 1 \cdot (x^{2} + 9)^{2}

Simplify

4 x (x^{2} + 9) (x - 9) + 1 \cdot (x^{2} + 9)^{2} : 5 x^{4} - 36 x^{3} + 54 x^{2} - 324 x + 81

= 5 x^{4} - 36 x^{3} + 54 x^{2} - 324 x + 81

(sin (t) cos (t))^{^{'}}

\frac{d ^{5}}{d x ^{5}} (x^{\frac{11}{2}})

x = 8 - y^{2}, x = y^{2}

\int x + 1 d x

x \to 0 lim (\frac{4}{x ^{3} ( x + 3 )})

What is the derivative of (x^2+9)^2(x-9) ?
The derivative of (x^2+9)^2(x-9) is 5x^4-36x^3+54x^2-324x+81
What is the first derivative of (x^2+9)^2(x-9) ?
The first derivative of (x^2+9)^2(x-9) is 5x^4-36x^3+54x^2-324x+81