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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\frac{d}{d x} ((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}

\int 2 - 2 cos (x) d x

4 x^{\frac{5}{4}} + 2 x^{\frac{3}{2}} + 4 x

\frac{3}{z ^{2}}

\int \frac{2 x - 1}{5 x ^{2} - x + 3} d x

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

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