What is the derivative of 7(x^2+3x)^6(2x+3) ?

The derivative of 7(x^2+3x)^6(2x+3) is 7(6(x^2+3x)^5(2x+3)^2+2(x^2+3x)^6)

What is the first derivative of 7(x^2+3x)^6(2x+3) ?

The first derivative of 7(x^2+3x)^6(2x+3) is 7(6(x^2+3x)^5(2x+3)^2+2(x^2+3x)^6)

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derivative of

7 (x^{2} + 3 x)^{6} (2 x + 3)

7 (6 (x^{2} + 3 x)^{5} (2 x + 3)^{2} + 2 (x^{2} + 3 x)^{6})

Solution steps

\frac{d}{d x} (7 (x^{2} + 3 x)^{6} (2 x + 3))

Take the constant out:

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

= 7 \frac{d}{d x} ((x^{2} + 3 x)^{6} (2 x + 3))

Apply the Product Rule:

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

f = (x^{2} + 3 x)^{6}, g = 2 x + 3

= 7 (\frac{d}{d x} ((x^{2} + 3 x)^{6}) (2 x + 3) + \frac{d}{d x} (2 x + 3) (x^{2} + 3 x)^{6})

\frac{d}{d x} ((x^{2} + 3 x)^{6}) = 6 (x^{2} + 3 x)^{5} (2 x + 3)

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

= 7 (6 (x^{2} + 3 x)^{5} (2 x + 3) (2 x + 3) + 2 (x^{2} + 3 x)^{6})

6 (x^{2} + 3 x)^{5} (2 x + 3) (2 x + 3) = 6 (x^{2} + 3 x)^{5} (2 x + 3)^{2}

= 7 (6 (x^{2} + 3 x)^{5} (2 x + 3)^{2} + 2 (x^{2} + 3 x)^{6})

y = \frac{3}{x ^{2}} - \frac{4}{x ^{3}}

\int e^{\frac{x}{60}} d x

\frac{d ^{2}}{d x ^{2}} (2 a x - x^{2})

x \to 4 lim (- (\frac{x}{x - 4}))

x^{4} a^{5} + y^{3} a + z^{6}

What is the derivative of 7(x^2+3x)^6(2x+3) ?
The derivative of 7(x^2+3x)^6(2x+3) is 7(6(x^2+3x)^5(2x+3)^2+2(x^2+3x)^6)
What is the first derivative of 7(x^2+3x)^6(2x+3) ?
The first derivative of 7(x^2+3x)^6(2x+3) is 7(6(x^2+3x)^5(2x+3)^2+2(x^2+3x)^6)