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Popular >

derivative of x^4(2x-5^6)

Solution

\frac{d}{d x} (x^{4} (2 x - 5)^{6})

Solution

4 x^{3} (2 x - 5)^{6} + 12 (2 x - 5)^{5} x^{4}

Solution steps

\frac{d}{d x} (x^{4} (2 x - 5)^{6})

Apply the Product Rule:

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

f = x^{4}, g = (2 x - 5)^{6}

= \frac{d}{d x} (x^{4}) (2 x - 5)^{6} + \frac{d}{d x} ((2 x - 5)^{6}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} ((2 x - 5)^{6}) = 12 (2 x - 5)^{5}

= 4 x^{3} (2 x - 5)^{6} + 12 (2 x - 5)^{5} x^{4}

Popular Examples

f(x)=(4x^2-1)/(x^3)

f (x) = \frac{4 x ^{2} - 1}{x ^{3}}

area x=sqrt(1/(12y)),y=x,x=16y area

x = \frac{1}{12 y}, y = x, x = 16 y

(\partial)/(\partial x)(-(x/y))

\frac{\partial}{\partial x} (- (\frac{x}{y}))

derivative of x/(4-sqrt(16-x^2))

\frac{d}{d x} (\frac{x}{4 - 16 - x ^{2}})

tangent of f(x)=5-2x^2,(-5,-45)tangent of

f (x) = 5 - 2 x^{2}, (- 5, - 45)

Frequently Asked Questions (FAQ)

What is the derivative of x^4(2x-5^6) ?
The derivative of x^4(2x-5^6) is 4x^3(2x-5)^6+12(2x-5)^5x^4
What is the first derivative of x^4(2x-5^6) ?
The first derivative of x^4(2x-5^6) is 4x^3(2x-5)^6+12(2x-5)^5x^4