What is the derivative of y=x(2x+3)^5 ?

The derivative of y=x(2x+3)^5 is (2x+3)^5+10x(2x+3)^4

What is the first derivative of y=x(2x+3)^5 ?

The first derivative of y=x(2x+3)^5 is (2x+3)^5+10x(2x+3)^4

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derivative of

y = x (2 x + 3)^{5}

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{\partial}{\partial x} (arcsin (x - y))

\int (x^{n}) d x

x e^{- x^{2}}

y^{^{'}} = - \frac{1}{2} y + x

\int_{0}^{2} π ((x - 1)^{2})^{2} d x

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