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

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

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

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

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derivative of

x (3 x + 4)^{5}

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

y = (x^{2} - 2 x + 2) e^{x}

(x^{3} + 1)^{5}

\int 4 x^{3} + 9 x^{2} y^{2} + 3 d x

n = 1 \sum \infty 7 - 6 (0.8)^{n}

\int 5 sin (2 x) d x

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