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

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

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

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

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derivative of

f (x) = (2 x + 3)^{6} \cdot (x - 2)^{4}

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((2 x + 3)^{6}) = 12 (2 x + 3)^{5}

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

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

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