Question

d/dx(x^5+x^7+x^9) =?​

Answer 1

Answer:

Let f(x)=x5(3−6x−9)

By Leibnitz product rule

f′(x)=x5dxd(3−6x−9)+(3−6x−9)dxd(x5)

=x3{0−6(−9)x−9−1}+(3−6x−9)(5x4)

=x3(54x−10)+15x4−30x−5

=54x−7+15x4−30x−5

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Answer 2

Answer:

The derivative of the given function is $\frac{d}{dx} (x^{5}+ x^{7}+ x^{9} )=5x^{4}+7x^{6}+9x^{8}$

Step-by-step explanation:

We are asked to differentiate a function.Let the given function be

$f(x)=x^{5} +x^{7}+ x^{9}$

As the powers of x are raised to certain integers,we shall use the formula for differentiating x raised to the power of n as shown-

$\frac{d}{dx} (x^{n} )=n.x^{n-1}$

Differentiating the given function based on the above formula,we get

$\frac{d}{dx} (x^{5} )=5.x^{5-1}=5x^{4}\\\frac{d}{dx} (x^{7} )=7.x^{7-1}=7x^{6}\\\frac{d}{dx} (x^{9} )=9.x^{9-1}=9x^{8}$

Adding all the terms of above,we get the derivative as

$\frac{d}{dx} (x^{5}+ x^{7}+ x^{9} )=5x^{4}+7x^{6}+9x^{8}$

Therefore,the derivative of the given function is $\frac{d}{dx} (x^{5}+ x^{7}+ x^{9} )=5x^{4}+7x^{6}+9x^{8}$

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