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

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derivative of

x^{4} (2 x - 5)^{6}

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}

y^{^{''}} + 40 y^{^{'}} + 625 y = 0

\frac{s ^{2} + 1}{s ^{2} + 4}

\int_{0}^{1} \frac{17}{x ^{5}} d x

\int x x^{2} + 2 x + 2 d x

\int x sin (- 2 x) d x

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