What is the derivative of 5^{(6x^2-7x(8x^2+9)}) ?

The derivative of 5^{(6x^2-7x(8x^2+9)}) is ln(5)*5^{(6x^2-7x)(8x^2+9)}(192x^3-168x^2+108x-63)

What is the first derivative of 5^{(6x^2-7x(8x^2+9)}) ?

The first derivative of 5^{(6x^2-7x(8x^2+9)}) is ln(5)*5^{(6x^2-7x)(8x^2+9)}(192x^3-168x^2+108x-63)

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\frac{d}{d x} (5^{(6 x^{2} - 7 x) (8 x^{2} + 9)})

ln (5) \cdot 5^{(6 x^{2} - 7 x) (8 x^{2} + 9)} (192 x^{3} - 168 x^{2} + 108 x - 63)

Solution steps

\frac{d}{d x} (5^{(6 x^{2} - 7 x) (8 x^{2} + 9)})

Apply exponent rule:

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

5^{(6 x^{2} - 7 x) (8 x^{2} + 9)} = e^{(6 x^{2} - 7 x) (8 x^{2} + 9) l n (5)}

= \frac{d}{d x} (e^{(6 x^{2} - 7 x) (8 x^{2} + 9) l n (5)})

Apply the chain rule:

e^{(6 x^{2} - 7 x) (8 x^{2} + 9) l n (5)} \frac{d}{d x} ((6 x^{2} - 7 x) (8 x^{2} + 9) ln (5))

= e^{(6 x^{2} - 7 x) (8 x^{2} + 9) l n (5)} \frac{d}{d x} ((6 x^{2} - 7 x) (8 x^{2} + 9) ln (5))

\frac{d}{d x} ((6 x^{2} - 7 x) (8 x^{2} + 9) ln (5)) = ln (5) (192 x^{3} - 168 x^{2} + 108 x - 63)

= e^{(6 x^{2} - 7 x) (8 x^{2} + 9) l n (5)} ln (5) (192 x^{3} - 168 x^{2} + 108 x - 63)

e^{(6 x^{2} - 7 x) (8 x^{2} + 9) l n (5)} = 5^{(6 x^{2} - 7 x) (8 x^{2} + 9)}

= ln (5) \cdot 5^{(6 x^{2} - 7 x) (8 x^{2} + 9)} (192 x^{3} - 168 x^{2} + 108 x - 63)

\int - 2 x + 9 x^{2} - 4 x^{3} + 16 d x

\int e^{7 x} sin (3 x) d x

\int 8 tan^{3} (x) sec (x) d x

\frac{d}{d x} (3 x^{2} - 10)

x^{2} y^{^{''}} - 7 x y^{^{'}} + 15 y = 0, y (1) = 0, y^{^{'}} (1) = 2

What is the derivative of 5^{(6x^2-7x(8x^2+9)}) ?
The derivative of 5^{(6x^2-7x(8x^2+9)}) is ln(5)*5^{(6x^2-7x)(8x^2+9)}(192x^3-168x^2+108x-63)
What is the first derivative of 5^{(6x^2-7x(8x^2+9)}) ?
The first derivative of 5^{(6x^2-7x(8x^2+9)}) is ln(5)*5^{(6x^2-7x)(8x^2+9)}(192x^3-168x^2+108x-63)