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

The derivative of (3x^3+1(-4x^2-3)^4) is 9x^2(-4x^2-3)^4-32x(-4x^2-3)^3(3x^3+1)

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

The first derivative of (3x^3+1(-4x^2-3)^4) is 9x^2(-4x^2-3)^4-32x(-4x^2-3)^3(3x^3+1)

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

9 x^{2} (- 4 x^{2} - 3)^{4} - 32 x (- 4 x^{2} - 3)^{3} (3 x^{3} + 1)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (3 x^{3} + 1) = 9 x^{2}

\frac{d}{d x} ((- 4 x^{2} - 3)^{4}) = - 32 x (- 4 x^{2} - 3)^{3}

= 9 x^{2} (- 4 x^{2} - 3)^{4} + (- 32 x (- 4 x^{2} - 3)^{3}) (3 x^{3} + 1)

Simplify

= 9 x^{2} (- 4 x^{2} - 3)^{4} - 32 x (- 4 x^{2} - 3)^{3} (3 x^{3} + 1)

x \to 4 lim (\frac{x ^{2} - 6}{x - 4})

\int \frac{t}{1 + t} d t

14 \cdot (\frac{- x + 2}{x ^{2}})

x \to 0 lim (\frac{e ^{7 x} - 1}{x})

\int e^{3 y} d y

What is the derivative of (3x^3+1(-4x^2-3)^4) ?
The derivative of (3x^3+1(-4x^2-3)^4) is 9x^2(-4x^2-3)^4-32x(-4x^2-3)^3(3x^3+1)
What is the first derivative of (3x^3+1(-4x^2-3)^4) ?
The first derivative of (3x^3+1(-4x^2-3)^4) is 9x^2(-4x^2-3)^4-32x(-4x^2-3)^3(3x^3+1)