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Popular >

derivative of x^5(2x-1^7)

Solution

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

Solution

5 x^{4} (2 x - 1)^{7} + 14 (2 x - 1)^{6} x^{5}

Solution steps

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

Apply the Product Rule:

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

f = x^{5}, g = (2 x - 1)^{7}

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} ((2 x - 1)^{7}) = 14 (2 x - 1)^{6}

= 5 x^{4} (2 x - 1)^{7} + 14 (2 x - 1)^{6} x^{5}

Popular Examples

derivative of (x+7/(x^3+x-6))

\frac{d}{d x} (\frac{x + 7}{x ^{3} + x - 6})

limit as x approaches 1 of |-x^2+1|

x \to 1 lim (- x^{2} + 1)

x*(dy)/(dx)+7y= 1/x

x \cdot \frac{d y}{d x} + 7 y = \frac{1}{x}

integral of e^{5x}sin(5x)

\int e^{5 x} sin (5 x) d x

area y=cos(x),x= pi/4 ,x= pi/3 area

y = cos (x), x = \frac{π}{4}, x = \frac{π}{3}

Frequently Asked Questions (FAQ)

What is the derivative of x^5(2x-1^7) ?
The derivative of x^5(2x-1^7) is 5x^4(2x-1)^7+14(2x-1)^6x^5
What is the first derivative of x^5(2x-1^7) ?
The first derivative of x^5(2x-1^7) is 5x^4(2x-1)^7+14(2x-1)^6x^5