What is the derivative of (4x-5)^3(1-x^5)^2 ?

The derivative of (4x-5)^3(1-x^5)^2 is 12(4x-5)^2(1-x^5)^2-10x^4(1-x^5)(4x-5)^3

What is the first derivative of (4x-5)^3(1-x^5)^2 ?

The first derivative of (4x-5)^3(1-x^5)^2 is 12(4x-5)^2(1-x^5)^2-10x^4(1-x^5)(4x-5)^3

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derivative of

(4 x - 5)^{3} (1 - x^{5})^{2}

12 (4 x - 5)^{2} (1 - x^{5})^{2} - 10 x^{4} (1 - x^{5}) (4 x - 5)^{3}

Solution steps

\frac{d}{d x} ((4 x - 5)^{3} (1 - x^{5})^{2})

Apply the Product Rule:

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

f = (4 x - 5)^{3}, g = (1 - x^{5})^{2}

= \frac{d}{d x} ((4 x - 5)^{3}) (1 - x^{5})^{2} + \frac{d}{d x} ((1 - x^{5})^{2}) (4 x - 5)^{3}

\frac{d}{d x} ((4 x - 5)^{3}) = 12 (4 x - 5)^{2}

\frac{d}{d x} ((1 - x^{5})^{2}) = - 10 x^{4} (1 - x^{5})

= 12 (4 x - 5)^{2} (1 - x^{5})^{2} + (- 10 x^{4} (1 - x^{5})) (4 x - 5)^{3}

Simplify

= 12 (4 x - 5)^{2} (1 - x^{5})^{2} - 10 x^{4} (1 - x^{5}) (4 x - 5)^{3}

y^{^{'}} = (x + y)^{2}, y (0) = 1

sin (x)

\frac{\partial}{\partial x} (2 + y ln (4 + x (y)^{2}))

\frac{d}{d x} (\frac{x y sin ( x - y )}{1 + x ^{2} + y ^{2}})

f (x) = 3^{s i n (3 x)}

What is the derivative of (4x-5)^3(1-x^5)^2 ?
The derivative of (4x-5)^3(1-x^5)^2 is 12(4x-5)^2(1-x^5)^2-10x^4(1-x^5)(4x-5)^3
What is the first derivative of (4x-5)^3(1-x^5)^2 ?
The first derivative of (4x-5)^3(1-x^5)^2 is 12(4x-5)^2(1-x^5)^2-10x^4(1-x^5)(4x-5)^3