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

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

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

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

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derivative of

y = (x^{2} + 3 x)^{4}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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