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

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

The first derivative of (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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\frac{d}{d x} ((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}

y^{^{''}} - 4 y = 6 e^{- x}

\int_{0}^{1} \frac{x}{x ^{2} + 1} d x

y^{4} x^{2} y^{^{'}} = 1

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

4 e^{x} cos (x)

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