What is the derivative of 12^{0.5}-x^{1.5} ?

The derivative of 12^{0.5}-x^{1.5} is -1.5x^{1/2}

What is the first derivative of 12^{0.5}-x^{1.5} ?

The first derivative of 12^{0.5}-x^{1.5} is -1.5x^{1/2}

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derivative of

1 2^{0.5} - x^{1.5}

- 1.5 x^{\frac{1}{2}}

Solution steps

\frac{d}{d x} (1 2^{0.5} - x^{1.5})

Simplify

1 2^{0.5} - x^{1.5} : 3.46410 \dots - x^{1.5}

= \frac{d}{d x} (3.46410 \dots - x^{1.5})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3.46410 \dots) - \frac{d}{d x} (x^{1.5})

\frac{d}{d x} (3.46410 \dots) = 0

\frac{d}{d x} (x^{1.5}) = 1.5 x^{0.5}

= 0 - 1.5 x^{0.5}

Simplify

= - 1.5 x^{\frac{1}{2}}

What is the derivative of 12^{0.5}-x^{1.5} ?
The derivative of 12^{0.5}-x^{1.5} is -1.5x^{1/2}
What is the first derivative of 12^{0.5}-x^{1.5} ?
The first derivative of 12^{0.5}-x^{1.5} is -1.5x^{1/2}