What is the derivative of f(x)=sqrt(x+1)(1-5x^2)^8 ?

The derivative of f(x)=sqrt(x+1)(1-5x^2)^8 is ((1-5x^2)^8)/(2sqrt(x+1))-80x(1-5x^2)^7sqrt(x+1)

What is the first derivative of f(x)=sqrt(x+1)(1-5x^2)^8 ?

The first derivative of f(x)=sqrt(x+1)(1-5x^2)^8 is ((1-5x^2)^8)/(2sqrt(x+1))-80x(1-5x^2)^7sqrt(x+1)

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derivative of

f (x) = x + 1 (1 - 5 x^{2})^{8}

\frac{( 1 - 5 x ^{2} ) ^{8}}{2 x + 1} - 80 x (1 - 5 x^{2})^{7} x + 1

Solution steps

\frac{d}{d x} (x + 1 (1 - 5 x^{2})^{8})

Apply the Product Rule:

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

f = x + 1, g = (1 - 5 x^{2})^{8}

= \frac{d}{d x} (x + 1) (1 - 5 x^{2})^{8} + \frac{d}{d x} ((1 - 5 x^{2})^{8}) x + 1

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

\frac{d}{d x} ((1 - 5 x^{2})^{8}) = - 80 x (1 - 5 x^{2})^{7}

= \frac{1}{2 x + 1} (1 - 5 x^{2})^{8} + (- 80 x (1 - 5 x^{2})^{7}) x + 1

Simplify

\frac{1}{2 x + 1} (1 - 5 x^{2})^{8} + (- 80 x (1 - 5 x^{2})^{7}) x + 1 : \frac{( 1 - 5 x ^{2} ) ^{8}}{2 x + 1} - 80 x (1 - 5 x^{2})^{7} x + 1

= \frac{( 1 - 5 x ^{2} ) ^{8}}{2 x + 1} - 80 x (1 - 5 x^{2})^{7} x + 1

\int \frac{1}{49 - x ^{2}} d x

y^{^{'}} = - y sin (2 x)

y = 4 e^{x} cos (x), 4, at x = 0

\frac{d y}{d x} y = 4 x^{2} + 2

\frac{5}{s}

What is the derivative of f(x)=sqrt(x+1)(1-5x^2)^8 ?
The derivative of f(x)=sqrt(x+1)(1-5x^2)^8 is ((1-5x^2)^8)/(2sqrt(x+1))-80x(1-5x^2)^7sqrt(x+1)
What is the first derivative of f(x)=sqrt(x+1)(1-5x^2)^8 ?
The first derivative of f(x)=sqrt(x+1)(1-5x^2)^8 is ((1-5x^2)^8)/(2sqrt(x+1))-80x(1-5x^2)^7sqrt(x+1)