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Popular >

derivative of y=x(3x+2)^5

Solution

derivative of

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

Solution

(3 x + 2)^{5} + 15 x (3 x + 2)^{4}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((3 x + 2)^{5}) = 15 (3 x + 2)^{4}

= 1 \cdot (3 x + 2)^{5} + 15 (3 x + 2)^{4} x

Simplify

= (3 x + 2)^{5} + 15 x (3 x + 2)^{4}

Popular Examples

tangent of f(x)= 8/(x^2+x+2),\at x=2 tangent of

f (x) = \frac{8}{x ^{2} + x + 2}, at x = 2

t^2(dy)/(dt)+4ty-y^3=0

t^{2} \frac{d y}{d t} + 4 t y - y^{3} = 0

limit as h approaches+0 of 2x+h

h \to + 0 lim (2 x + h)

(\partial)/(\partial x)(ln(x^3+y^5))

\frac{\partial}{\partial x} (ln (x^{3} + y^{5}))

(\partial)/(\partial y)((x+y)^2)

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

Frequently Asked Questions (FAQ)

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