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Popular >

derivative of y=x(3x+4)^5

Solution

derivative of

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

Solution

(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}

Popular Examples

derivative of y= 1/((x+1)^2)derivative of

y = \frac{1}{( x + 1 ) ^{2}}

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integral of (x^2-6x-17)/((x-1)^2(x^2+1))

\int \frac{x ^{2} - 6 x - 17}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

integral from 0 to 3 of (9-x^2)

\int_{0}^{3} (9 - x^{2}) d x

(\partial)/(\partial x)(3sqrt(xy^2+9x))

\frac{\partial}{\partial x} (3 x y^{2} + 9 x)

Frequently Asked Questions (FAQ)

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