What is the derivative of 6^{5x^4-10x^3+5} ?

The derivative of 6^{5x^4-10x^3+5} is ln(6)*6^{5x^4-10x^3+5}(20x^3-30x^2)

What is the first derivative of 6^{5x^4-10x^3+5} ?

The first derivative of 6^{5x^4-10x^3+5} is ln(6)*6^{5x^4-10x^3+5}(20x^3-30x^2)

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\frac{d}{d x} (6^{5 x^{4} - 10 x^{3} + 5})

ln (6) \cdot 6^{5 x^{4} - 10 x^{3} + 5} (20 x^{3} - 30 x^{2})

Solution steps

\frac{d}{d x} (6^{5 x^{4} - 10 x^{3} + 5})

Apply exponent rule:

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

6^{5 x^{4} - 10 x^{3} + 5} = e^{(5 x^{4} - 10 x^{3} + 5) l n (6)}

= \frac{d}{d x} (e^{(5 x^{4} - 10 x^{3} + 5) l n (6)})

Apply the chain rule:

e^{(5 x^{4} - 10 x^{3} + 5) l n (6)} \frac{d}{d x} ((5 x^{4} - 10 x^{3} + 5) ln (6))

= e^{(5 x^{4} - 10 x^{3} + 5) l n (6)} \frac{d}{d x} ((5 x^{4} - 10 x^{3} + 5) ln (6))

\frac{d}{d x} ((5 x^{4} - 10 x^{3} + 5) ln (6)) = ln (6) (20 x^{3} - 30 x^{2})

= e^{(5 x^{4} - 10 x^{3} + 5) l n (6)} ln (6) (20 x^{3} - 30 x^{2})

e^{(5 x^{4} - 10 x^{3} + 5) l n (6)} = 6^{5 x^{4} - 10 x^{3} + 5}

= ln (6) \cdot 6^{5 x^{4} - 10 x^{3} + 5} (20 x^{3} - 30 x^{2})

What is the derivative of 6^{5x^4-10x^3+5} ?
The derivative of 6^{5x^4-10x^3+5} is ln(6)*6^{5x^4-10x^3+5}(20x^3-30x^2)
What is the first derivative of 6^{5x^4-10x^3+5} ?
The first derivative of 6^{5x^4-10x^3+5} is ln(6)*6^{5x^4-10x^3+5}(20x^3-30x^2)