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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((2 x - 3)^{5}) = 10 (2 x - 3)^{4}

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

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

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