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

The derivative of (-2x-3^5(3x+1)^3) is -10(-2x-3)^4(3x+1)^3+9(3x+1)^2(-2x-3)^5

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

The first derivative of (-2x-3^5(3x+1)^3) is -10(-2x-3)^4(3x+1)^3+9(3x+1)^2(-2x-3)^5

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

- 10 (- 2 x - 3)^{4} (3 x + 1)^{3} + 9 (3 x + 1)^{2} (- 2 x - 3)^{5}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= (- 10 (- 2 x - 3)^{4}) (3 x + 1)^{3} + 9 (3 x + 1)^{2} (- 2 x - 3)^{5}

Simplify

= - 10 (- 2 x - 3)^{4} (3 x + 1)^{3} + 9 (3 x + 1)^{2} (- 2 x - 3)^{5}

n = 2 \sum \infty ln (n)

t \to 0 lim (ln (t))

\int cot (t) sin^{2} (t) - 25 d t

\int 1 - sin^{2} (x) d x

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

What is the derivative of (-2x-3^5(3x+1)^3) ?
The derivative of (-2x-3^5(3x+1)^3) is -10(-2x-3)^4(3x+1)^3+9(3x+1)^2(-2x-3)^5
What is the first derivative of (-2x-3^5(3x+1)^3) ?
The first derivative of (-2x-3^5(3x+1)^3) is -10(-2x-3)^4(3x+1)^3+9(3x+1)^2(-2x-3)^5