What is the derivative of (2x^2-1^3(x^4+3)^5) ?

The derivative of (2x^2-1^3(x^4+3)^5) is 12x(2x^2-1)^2(x^4+3)^5+20x^3(x^4+3)^4(2x^2-1)^3

What is the first derivative of (2x^2-1^3(x^4+3)^5) ?

The first derivative of (2x^2-1^3(x^4+3)^5) is 12x(2x^2-1)^2(x^4+3)^5+20x^3(x^4+3)^4(2x^2-1)^3

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\frac{d}{d x} ((2 x^{2} - 1)^{3} (x^{4} + 3)^{5})

12 x (2 x^{2} - 1)^{2} (x^{4} + 3)^{5} + 20 x^{3} (x^{4} + 3)^{4} (2 x^{2} - 1)^{3}

Solution steps

\frac{d}{d x} ((2 x^{2} - 1)^{3} (x^{4} + 3)^{5})

Apply the Product Rule:

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

f = (2 x^{2} - 1)^{3}, g = (x^{4} + 3)^{5}

= \frac{d}{d x} ((2 x^{2} - 1)^{3}) (x^{4} + 3)^{5} + \frac{d}{d x} ((x^{4} + 3)^{5}) (2 x^{2} - 1)^{3}

\frac{d}{d x} ((2 x^{2} - 1)^{3}) = 12 x (2 x^{2} - 1)^{2}

\frac{d}{d x} ((x^{4} + 3)^{5}) = 20 x^{3} (x^{4} + 3)^{4}

= 12 x (2 x^{2} - 1)^{2} (x^{4} + 3)^{5} + 20 x^{3} (x^{4} + 3)^{4} (2 x^{2} - 1)^{3}

75 (1 - \frac{t}{24})^{2}

\int t sec^{2} (4 t) d t

y = x^{3} (2 x - 1)^{7}

\int x^{8} (x^{9} - 10)^{7} d x

\frac{\partial}{\partial y} (- 5 y z^{4})

What is the derivative of (2x^2-1^3(x^4+3)^5) ?
The derivative of (2x^2-1^3(x^4+3)^5) is 12x(2x^2-1)^2(x^4+3)^5+20x^3(x^4+3)^4(2x^2-1)^3
What is the first derivative of (2x^2-1^3(x^4+3)^5) ?
The first derivative of (2x^2-1^3(x^4+3)^5) is 12x(2x^2-1)^2(x^4+3)^5+20x^3(x^4+3)^4(2x^2-1)^3