What is the derivative of 3/4 x^2-5x^3 ?

The derivative of 3/4 x^2-5x^3 is (3x)/2-15x^2

What is the first derivative of 3/4 x^2-5x^3 ?

The first derivative of 3/4 x^2-5x^3 is (3x)/2-15x^2

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\frac{d}{d x} (\frac{3}{4} x^{2} - 5 x^{3})

\frac{3 x}{2} - 15 x^{2}

Solution steps

\frac{d}{d x} (\frac{3}{4} x^{2} - 5 x^{3})

Simplify

\frac{3}{4} x^{2} - 5 x^{3} : \frac{3 x ^{2}}{4} - 5 x^{3}

= \frac{d}{d x} (\frac{3 x ^{2}}{4} - 5 x^{3})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{3 x ^{2}}{4}) - \frac{d}{d x} (5 x^{3})

\frac{d}{d x} (\frac{3 x ^{2}}{4}) = \frac{3 x}{2}

\frac{d}{d x} (5 x^{3}) = 15 x^{2}

= \frac{3 x}{2} - 15 x^{2}

What is the derivative of 3/4 x^2-5x^3 ?
The derivative of 3/4 x^2-5x^3 is (3x)/2-15x^2
What is the first derivative of 3/4 x^2-5x^3 ?
The first derivative of 3/4 x^2-5x^3 is (3x)/2-15x^2