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

The derivative of (4x-1^3(5x+3)^2) is 12(4x-1)^2(5x+3)^2+10(5x+3)(4x-1)^3

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

The first derivative of (4x-1^3(5x+3)^2) is 12(4x-1)^2(5x+3)^2+10(5x+3)(4x-1)^3

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

12 (4 x - 1)^{2} (5 x + 3)^{2} + 10 (5 x + 3) (4 x - 1)^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((4 x - 1)^{3}) = 12 (4 x - 1)^{2}

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

= 12 (4 x - 1)^{2} (5 x + 3)^{2} + 10 (5 x + 3) (4 x - 1)^{3}

\int \frac{1}{( 1 + cos ^{2} ( x ) )} d x

e^{\frac{x}{2}}

3 x^{2} - 4

\frac{d y}{d x}, y^{3} = 4 x

What is the derivative of (4x-1^3(5x+3)^2) ?
The derivative of (4x-1^3(5x+3)^2) is 12(4x-1)^2(5x+3)^2+10(5x+3)(4x-1)^3
What is the first derivative of (4x-1^3(5x+3)^2) ?
The first derivative of (4x-1^3(5x+3)^2) is 12(4x-1)^2(5x+3)^2+10(5x+3)(4x-1)^3