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

The derivative of (2x-4^4(x^2+x+1)^5) is 8(2x-4)^3(x^2+x+1)^5+5(x^2+x+1)^4(2x+1)(2x-4)^4

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

The first derivative of (2x-4^4(x^2+x+1)^5) is 8(2x-4)^3(x^2+x+1)^5+5(x^2+x+1)^4(2x+1)(2x-4)^4

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

8 (2 x - 4)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 4)^{4}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((2 x - 4)^{4}) = 8 (2 x - 4)^{3}

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

= 8 (2 x - 4)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 4)^{4}

x^{2} (x - 4), [- 1, 5]

\int \frac{( 5 x + 3 )}{( x ^{2} + 4 x + 7 )} d x

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

k = 1 \sum \infty \frac{k}{k ^{2} + 1}

\int_{0}^{1 - y} 6 x d x

What is the derivative of (2x-4^4(x^2+x+1)^5) ?
The derivative of (2x-4^4(x^2+x+1)^5) is 8(2x-4)^3(x^2+x+1)^5+5(x^2+x+1)^4(2x+1)(2x-4)^4
What is the first derivative of (2x-4^4(x^2+x+1)^5) ?
The first derivative of (2x-4^4(x^2+x+1)^5) is 8(2x-4)^3(x^2+x+1)^5+5(x^2+x+1)^4(2x+1)(2x-4)^4