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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\frac{d}{d x} (e^{x} (x - 5) + 5)

x \frac{d y}{d x} - y = 6 x^{2}

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{t} + e^{- t}

\int_{0}^{64} \frac{1}{64 - x} d x

x, 4 x, - x + 22

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