What is the derivative of y=(5x-4)^5(3-x^3)^5 ?

The derivative of y=(5x-4)^5(3-x^3)^5 is 25(5x-4)^4(3-x^3)^5-15x^2(3-x^3)^4(5x-4)^5

What is the first derivative of y=(5x-4)^5(3-x^3)^5 ?

The first derivative of y=(5x-4)^5(3-x^3)^5 is 25(5x-4)^4(3-x^3)^5-15x^2(3-x^3)^4(5x-4)^5

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derivative of

y = (5 x - 4)^{5} (3 - x^{3})^{5}

25 (5 x - 4)^{4} (3 - x^{3})^{5} - 15 x^{2} (3 - x^{3})^{4} (5 x - 4)^{5}

Solution steps

\frac{d}{d x} ((5 x - 4)^{5} (3 - x^{3})^{5})

Apply the Product Rule:

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

f = (5 x - 4)^{5}, g = (3 - x^{3})^{5}

= \frac{d}{d x} ((5 x - 4)^{5}) (3 - x^{3})^{5} + \frac{d}{d x} ((3 - x^{3})^{5}) (5 x - 4)^{5}

\frac{d}{d x} ((5 x - 4)^{5}) = 25 (5 x - 4)^{4}

\frac{d}{d x} ((3 - x^{3})^{5}) = - 15 x^{2} (3 - x^{3})^{4}

= 25 (5 x - 4)^{4} (3 - x^{3})^{5} + (- 15 x^{2} (3 - x^{3})^{4}) (5 x - 4)^{5}

Simplify

= 25 (5 x - 4)^{4} (3 - x^{3})^{5} - 15 x^{2} (3 - x^{3})^{4} (5 x - 4)^{5}

f (x) = 2 x^{2} - 6 x, at x = 1

g (x) = 5 x + 20, at x = 1

4 x + 3

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 x}

x \to 3 lim (x 25 - x^{3})

What is the derivative of y=(5x-4)^5(3-x^3)^5 ?
The derivative of y=(5x-4)^5(3-x^3)^5 is 25(5x-4)^4(3-x^3)^5-15x^2(3-x^3)^4(5x-4)^5
What is the first derivative of y=(5x-4)^5(3-x^3)^5 ?
The first derivative of y=(5x-4)^5(3-x^3)^5 is 25(5x-4)^4(3-x^3)^5-15x^2(3-x^3)^4(5x-4)^5