What is the derivative of y=(2x-3)^4(x^2+x+1)^5 ?

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

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

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

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derivative of

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

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

Solution steps

\frac{d}{d x} ((2 x - 3)^{4} (x^{2} + x + 1)^{5})

Apply the Product Rule:

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

f = (2 x - 3)^{4}, g = (x^{2} + x + 1)^{5}

= \frac{d}{d x} ((2 x - 3)^{4}) (x^{2} + x + 1)^{5} + \frac{d}{d x} ((x^{2} + x + 1)^{5}) (2 x - 3)^{4}

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

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

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

\frac{d}{d x} (a^{6 x^{2}})

\int \frac{x ^{2}}{4 x} d x

x^{2} y^{^{'}} + 3 x y = e^{x}

2 y^{^{''}} - 2 y^{^{'}} + 13 y = 0

\frac{d}{d x} (- 4 sin^{3} (3 x))

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