How do you find the derivative of # 6x^(- 7/8)#?

Answer 1

#f'(x)=-21/4x^(-15/8)#

Before we derive this, we shall first remind ourselves of 2 important formulas, #f(x)=kh(x)\impliesf'(x)=kh'(x)# and #f(x)=x^n\impliesf'(x)=nx^(n-1)#

Now, we have #f(x)=6x^(-7/8)# From above equations, we take #k=6# and #g(x)=x^(-7/8)# So, #f'(x)=6*(d(x^(-7/8)))/dx\impliesf'(x)=-6*7/8*x^(-15/8)#

Simplifying provides the solution.

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Answer 2

Isaiah Allen

To find the derivative of (6x^{-7/8}), you can use the power rule for differentiation. The power rule states that if (f(x) = ax^n), then (f'(x) = anx^{n-1}). Applying this rule to (6x^{-7/8}), the derivative is:

[ f'(x) = \frac{-7}{8} \cdot 6x^{-7/8 - 1} ]

Simplify the expression:

[ f'(x) = \frac{-7}{8} \cdot 6x^{-7/8 - 1} = -\frac{7}{4}x^{-15/8} ]

So, the derivative of (6x^{-7/8}) is (-\frac{7}{4}x^{-15/8}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.