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

The derivative of (2q^2-3)^6(5q+4)^3 is 24q(2q^2-3)^5(5q+4)^3+15(5q+4)^2(2q^2-3)^6

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

The first derivative of (2q^2-3)^6(5q+4)^3 is 24q(2q^2-3)^5(5q+4)^3+15(5q+4)^2(2q^2-3)^6

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derivative of

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

24 q (2 q^{2} - 3)^{5} (5 q + 4)^{3} + 15 (5 q + 4)^{2} (2 q^{2} - 3)^{6}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d q} ((2 q^{2} - 3)^{6}) = 24 q (2 q^{2} - 3)^{5}

\frac{d}{d q} ((5 q + 4)^{3}) = 15 (5 q + 4)^{2}

= 24 q (2 q^{2} - 3)^{5} (5 q + 4)^{3} + 15 (5 q + 4)^{2} (2 q^{2} - 3)^{6}

What is the derivative of (2q^2-3)^6(5q+4)^3 ?
The derivative of (2q^2-3)^6(5q+4)^3 is 24q(2q^2-3)^5(5q+4)^3+15(5q+4)^2(2q^2-3)^6
What is the first derivative of (2q^2-3)^6(5q+4)^3 ?
The first derivative of (2q^2-3)^6(5q+4)^3 is 24q(2q^2-3)^5(5q+4)^3+15(5q+4)^2(2q^2-3)^6