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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

n = 1 \sum \infty \frac{3 n}{- 2 n + 5}

2 e^{3 t}

3600 (1 - \frac{t}{60})^{2}

x \to 3 lim (\frac{∣ x + 3 ∣}{x + 3})

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

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