What is the derivative of y=(3x+4)^5+15x(3x+4)^4 ?

The derivative of y=(3x+4)^5+15x(3x+4)^4 is 7290x^4+32400x^3+51840x^2+34560x+7680

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

The first derivative of y=(3x+4)^5+15x(3x+4)^4 is 7290x^4+32400x^3+51840x^2+34560x+7680

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derivative of

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

7290 x^{4} + 32400 x^{3} + 51840 x^{2} + 34560 x + 7680

Solution steps

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

Simplify

(3 x + 4)^{5} + 15 x (3 x + 4)^{4} : 1458 x^{5} + 8100 x^{4} + 17280 x^{3} + 17280 x^{2} + 7680 x + 1024

= \frac{d}{d x} (1458 x^{5} + 8100 x^{4} + 17280 x^{3} + 17280 x^{2} + 7680 x + 1024)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1458 x^{5}) + \frac{d}{d x} (8100 x^{4}) + \frac{d}{d x} (17280 x^{3}) + \frac{d}{d x} (17280 x^{2}) + \frac{d}{d x} (7680 x) + \frac{d}{d x} (1024)

\frac{d}{d x} (1458 x^{5}) = 7290 x^{4}

\frac{d}{d x} (8100 x^{4}) = 32400 x^{3}

\frac{d}{d x} (17280 x^{3}) = 51840 x^{2}

\frac{d}{d x} (17280 x^{2}) = 34560 x

\frac{d}{d x} (7680 x) = 7680

\frac{d}{d x} (1024) = 0

= 7290 x^{4} + 32400 x^{3} + 51840 x^{2} + 34560 x + 7680 + 0

Simplify

= 7290 x^{4} + 32400 x^{3} + 51840 x^{2} + 34560 x + 7680

\int - e^{4 x} d x

n = 1 \sum \infty \frac{n}{csc ( \frac{1}{n} )}

\int \frac{( arctan ( x ) ) ^{4}}{1 + x ^{2}} d x

\frac{\partial}{\partial x} (y ln (x^{3} + y^{4} + 2))

\frac{d}{d x} (e^{x z (x)})

What is the derivative of y=(3x+4)^5+15x(3x+4)^4 ?
The derivative of y=(3x+4)^5+15x(3x+4)^4 is 7290x^4+32400x^3+51840x^2+34560x+7680
What is the first derivative of y=(3x+4)^5+15x(3x+4)^4 ?
The first derivative of y=(3x+4)^5+15x(3x+4)^4 is 7290x^4+32400x^3+51840x^2+34560x+7680