What is the derivative of-10^{3x^2-4} ?

The derivative of-10^{3x^2-4} is -3ln(10)*5^{3x^2-4}*2^{3x^2-3}x

What is the first derivative of-10^{3x^2-4} ?

The first derivative of-10^{3x^2-4} is -3ln(10)*5^{3x^2-4}*2^{3x^2-3}x

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\frac{d}{d x} (- 1 0^{3 x^{2} - 4})

- 3 ln (10) \cdot 5^{3 x^{2} - 4} \cdot 2^{3 x^{2} - 3} x

Solution steps

\frac{d}{d x} (- 1 0^{3 x^{2} - 4})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (1 0^{3 x^{2} - 4})

Apply exponent rule:

a^{b} = e^{b l n (a)}

1 0^{3 x^{2} - 4} = e^{(3 x^{2} - 4) l n (10)}

= - \frac{d}{d x} (e^{(3 x^{2} - 4) l n (10)})

Apply the chain rule:

e^{(3 x^{2} - 4) l n (10)} \frac{d}{d x} ((3 x^{2} - 4) ln (10))

= e^{(3 x^{2} - 4) l n (10)} \frac{d}{d x} ((3 x^{2} - 4) ln (10))

\frac{d}{d x} ((3 x^{2} - 4) ln (10)) = 6 ln (10) x

= - e^{(3 x^{2} - 4) l n (10)} \cdot 6 ln (10) x

Simplify

- e^{(3 x^{2} - 4) l n (10)} \cdot 6 ln (10) x : - 3 ln (10) \cdot 5^{3 x^{2} - 4} \cdot 2^{3 x^{2} - 3} x

= - 3 ln (10) \cdot 5^{3 x^{2} - 4} \cdot 2^{3 x^{2} - 3} x

x \frac{d y}{d x} = e^{y + x}

f (x) = x - x^{3}, (1, 0)

x^{2} + 2 x y - y^{2} + x = 27, (4, 7)

\frac{d y}{d x} = \frac{y ^{3}}{1 - 2 x y ^{2}}, y (0) = 1

What is the derivative of-10^{3x^2-4} ?
The derivative of-10^{3x^2-4} is -3ln(10)*5^{3x^2-4}*2^{3x^2-3}x
What is the first derivative of-10^{3x^2-4} ?
The first derivative of-10^{3x^2-4} is -3ln(10)*5^{3x^2-4}*2^{3x^2-3}x