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DochEvi [55]
3 years ago
8

In Exercise find the derivative of the functions. f(x) = (4x - 3)(x2 + 9)

Mathematics
1 answer:
pashok25 [27]3 years ago
7 0

Answer: f'(x)=12x^2 - 6x+36

Step-by-step explanation:

According to the product rule of derivatives.

f'(x)=u'(x)v(x)+u(x)v'(x)

The given function : f(x) = (4x - 3)(x^2 + 9)

here , u(x) = 4x - 3 and v(x)=x^2 + 9

Differentiate both sides with respect to x, we get

u'(x) = 4+0=4 and v(x)=2x +0=2x

[\because \dfrac{d(ax)}{dx}=a\ , \dfrac{d(a)}{dx}=0 \ \&\ \ \dfrac{d(x^n)}{dx}=nx^{n-1}]

Then, Tge derivative of  withe respect to x will be :

f'(x)=u'(x)v(x)+u(x)v'(x)

=4(x^2 + 9)+( 4x - 3)(2x)

=4x^2 +36+8x^2 - 6x

=12x^2 - 6x+36

Hence, the derivative of the function is f'(x)=12x^2 - 6x+36 .

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6 have visited a zoo.

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Of the 6 who visited a factory, 3 also visited a zoo.

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