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

The derivative of 4x(3x-2^5) is 4((3x-2)^5+15x(3x-2)^4)

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

The first derivative of 4x(3x-2^5) is 4((3x-2)^5+15x(3x-2)^4)

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

= 4 (1 \cdot (3 x - 2)^{5} + 15 (3 x - 2)^{4} x)

Simplify

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

x \to 0 lim (x - 1)

\int (2 - x^{2})^{\frac{1}{2}} d x

y^{^{'}} = - y tan (t) + \frac{tan ( t )}{cos ( t )}

1 + 3 x, 3 \leq x \leq 9

\frac{d}{d x} (- 27 cos (3 x))

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