Get the answer to "Find the derivatives of the functions w=1z1.4+πz" - Plainmath

usagirl007A

Answered question

2021-10-18

Find the derivatives of the functions

w = \frac{1}{z^{1.4}} + \frac{π}{\sqrt{z}}

Answer & Explanation

stuth1

Skilled2021-10-19Added 97 answers

Step 1
Given function is

w = \frac{1}{z^{1.4}} + \frac{π}{\sqrt{z}}

To find the derivative of the functions.
Solution:
Power rule of differentiation states that:

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

Differentiating the given function with respect to z,

\frac{d w}{d z} = \frac{d}{d z} [\frac{1}{z^{1.4}} + \frac{π}{\sqrt{z}}]

= \frac{d}{d z} [z^{- 1.4} + π z^{- \frac{1}{2}}]

= - 1.4 z^{- 1.4 - 1} + π \cdot (- \frac{1}{2}) z^{- \frac{1}{2} - 1}

= - 1.4 z^{- 2.4} - \frac{π}{2} z^{- \frac{3}{2}}

= \frac{- 1.4}{z^{2.4}} - \frac{π}{2 z^{\frac{3}{2}}}

Step 2
Hence, derivative of the given function is

\frac{d w}{d z} = - \frac{1.4}{z^{2.4}} - \frac{π}{2 \sqrt{z^{3}}}

.

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