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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

f (x) = x^{3} - 2 x^{2} + 5

f (x) = 3 x^{3} + 6 x^{2} + 7 x

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

\int 2 x sin (x) d x

y^{^{'}} + 8 y = t + e^{- 7 t}

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