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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((2 x - 5)^{4}) = 8 (2 x - 5)^{3}

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

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

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

\frac{d}{d x} (ln (2 x))

y^{^{''}} - 5 y^{^{'}} + 4 y = 8 e^{x}

\int_{- 2}^{2} x d x

f (x) = - x^{2} + 16 x + 63, at x = 2

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