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

The derivative of f(x)=(x-5)^6(x+3)^2 is 6(x-5)^5(x+3)^2+2(x+3)(x-5)^6

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

The first derivative of f(x)=(x-5)^6(x+3)^2 is 6(x-5)^5(x+3)^2+2(x+3)(x-5)^6

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((x - 5)^{6}) = 6 (x - 5)^{5}

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

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

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