Differentiate?

**MathKidd** · March 28th 2010, 10:27 PM

1.Equation: $f(x)=3ln(3-7x)$
Solution: [tex]f'(x)=(3*-7)*\frac{u'}{u}
= $f'(x)=\frac{-21}{2-7x}$

2.Equation: $f(x)=e^{5x+2}$
solution: $f'(x)=5e^{5x+2}$

3. Equation: $g(x)=7^{x-3}+25$
Solution: $g'(x)=7^{x-3}Log7$

4. Equation: $f(x)=Log3x-Ln3$
Solution: $f'(x)=\frac{1}{x Log3}$

5. Equation: $h(x)=log2(5x+4)$
Solution: $h'(x)=\frac{5}{(5x+4)(log2)}$

6. Equation: $y= Ln \frac{(x-2)^4}{(1+x)^5}$
Solution: Unsure of how to solve

Derivative of

1. Equation= $a^x$
Solution=???

2 Equation= $e^u$
Solution= $a^u*u^1 = u^1*e^x$ or is it $e^u$

3 Equation = $a^u$
solution = ???

4. Find Result
Equation $Ln*\frac{u^4*}{z^6}$
Solution = $\frac{1}{x}*\frac{(u^4*v)(6z^5)-(4u^5)(z^6)}{(z^6)^2}$

**harish21** · March 28th 2010, 11:16 PM

Originally Posted by MathKidd

Is differentiate the same as derivatives? and is this question correct?

Problem: $f(x)=e$ Raised to the power of or ^ (5x+2)
Solution: = $5e$ Raised to the power of or ^ (5x+2)
or would it be written as $f1(x)=5e$ Raised to the power of or ^ (5x+2) (Assuming differentiate and derivatives are the same.)

Yes differentiate is the same as finding the derivative, Now to your question:

$f(x)=e^{5x+2}$ . Your latex input seems incorrect, but I guess this is what you are asking.

so,

$f'(x) = 5 \times e^{5x+2}$

and we come to the conclusion that your answer is correct!