What is the derivative of f(x)=x^6(6x^3+x)^5 ?

The derivative of f(x)=x^6(6x^3+x)^5 is 6x^5(6x^3+x)^5+5(6x^3+x)^4(18x^2+1)x^6

What is the first derivative of f(x)=x^6(6x^3+x)^5 ?

The first derivative of f(x)=x^6(6x^3+x)^5 is 6x^5(6x^3+x)^5+5(6x^3+x)^4(18x^2+1)x^6

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derivative of

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

6 x^{5} (6 x^{3} + x)^{5} + 5 (6 x^{3} + x)^{4} (18 x^{2} + 1) x^{6}

Solution steps

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

Apply the Product Rule:

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

f = x^{6}, g = (6 x^{3} + x)^{5}

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

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

\frac{d}{d x} ((6 x^{3} + x)^{5}) = 5 (6 x^{3} + x)^{4} (18 x^{2} + 1)

= 6 x^{5} (6 x^{3} + x)^{5} + 5 (6 x^{3} + x)^{4} (18 x^{2} + 1) x^{6}

f (x) = e^{3 x} \cdot ln (4 x)

\frac{\partial}{\partial x} (- y e^{x^{3}})

n = 1 \sum \infty (\frac{7}{8})^{n}

\int 5 cos (5 x) d x

\frac{\partial}{\partial x} (V (x))

What is the derivative of f(x)=x^6(6x^3+x)^5 ?
The derivative of f(x)=x^6(6x^3+x)^5 is 6x^5(6x^3+x)^5+5(6x^3+x)^4(18x^2+1)x^6
What is the first derivative of f(x)=x^6(6x^3+x)^5 ?
The first derivative of f(x)=x^6(6x^3+x)^5 is 6x^5(6x^3+x)^5+5(6x^3+x)^4(18x^2+1)x^6