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Popular >

derivative of f(x)=x^a(1-x)^b

Solution

derivative of

f (x) = x^{a} (1 - x)^{b}

Solution

a x^{a - 1} (1 - x)^{b} - b x^{a} (1 - x)^{b - 1}

Solution steps

\frac{d}{d x} (x^{a} (1 - x)^{b})

Apply the Product Rule:

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

f = x^{a}, g = (1 - x)^{b}

= \frac{d}{d x} (x^{a}) (1 - x)^{b} + \frac{d}{d x} ((1 - x)^{b}) x^{a}

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

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

= a x^{a - 1} (1 - x)^{b} + (- b (1 - x)^{b - 1}) x^{a}

Simplify

= a x^{a - 1} (1 - x)^{b} - b x^{a} (1 - x)^{b - 1}

Popular Examples

tangent of f(x)=9-4x+6x^2,\at x=8 tangent of

f (x) = 9 - 4 x + 6 x^{2}, at x = 8

(\partial)/(\partial y)(y^2e^{xy^2})

\frac{\partial}{\partial y} (y^{2} e^{x y^{2}})

integral of zsin(x)

\int z sin (x) d y

tangent of 1/3 x^3+7/2 x^2-3x+5 tangent of

\frac{1}{3} x^{3} + \frac{7}{2} x^{2} - 3 x + 5

f (t) = tan (t)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^a(1-x)^b ?
The derivative of f(x)=x^a(1-x)^b is ax^{a-1}(1-x)^b-bx^a(1-x)^{b-1}
What is the first derivative of f(x)=x^a(1-x)^b ?
The first derivative of f(x)=x^a(1-x)^b is ax^{a-1}(1-x)^b-bx^a(1-x)^{b-1}