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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((3 - 2 x)^{5}) = - 10 (3 - 2 x)^{4}

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

Simplify

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

y^{^{''}} + 4 y = t^{2} e^{3 t} + 3

x y^{^{'}} = y^{2} + 1

\frac{d y}{d x} + 3 y = x + e^{- 2 x}

\frac{3}{s + 2}

(\frac{x}{1 + x ^{2}})^{^{'}}

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