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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((2 x - 1)^{5}) = 10 (2 x - 1)^{4}

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

\int_{0}^{x} (sin^{2} (t)) d t

\frac{d y}{d x} = - 0.13 \cdot (100 - y)

n = 0 \sum \infty \frac{n}{( n + 1 )}

\int 3 x y + 2 d y

(- 1, 2), (4, 0)

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