Simplify the numerator.( -12t^((-3)2))Move the negative in front of the fraction.( -12t^(-32))Rewrite the expression using the negative exponent rule ( b^(-n)=1(b^n)).( -12⋅ 1(t^(32)))Combineterms.( -1(2t^(32)))反馈 收藏 ...
Derivative of a Fraction: Simplifying with Polynomial Division? Homework Statement if $$y = \frac{2x^5-3x^3+x^2}{x^3}$$ then $$\frac{dy}{dx} =$$ Homework Equations if $$f(x) = x^n$$ then $$f'(x) = nx^{n-1}$$ The Attempt at a Solution $$\frac{2x^5-3x^3+x^2...
Next, we can apply the Constant Multiple and Power Rule to each piece. Note that {eq}\sqrt{x} {/eq} can be written with a fraction exponent as {eq}x^\frac{1}{2} {/eq}, which gives it a compatible form to use the Power Rule on. Thus, we have: ...
Examples Differentiate all of the following functions. a. d f ' ?x? ? dx ?x 8 ?? 8x 8?1 ? 8 x 7 f ?x ? ? x 8 1. Bring down the exponent 2. Leave the base alone 3. Subtract one from the original exponent. ?? b. g?u? ? um ?? ??? ?? m d g' ?u? ? du ?u...
No, the derivative of e^x is not the same as the derivative of x^e. The derivative of e^x is e^x itself, while the derivative of x^e is e^x * x^(e-1). This is because the power rule for derivatives only applies when the base is a constant, not when the exponent is a ...
Move the negative in front of thefraction. 4(−12x−32)4(-12x-32) Combinex−32x-32and1212. 4(−x−322)4(-x-322) Multiply−1-1by44. −4x−322-4x-322 Combine−4-4andx−322x-322. −4x−322-4x-322 Movex−32x-32to thedenominatorusing the negativeexponentruleb...
Step 5 Simplify. Tap for more steps... Step 5.1 Rewrite the expression using the negative exponent rule . Step 5.2 Combine terms. Tap for more steps... Step 5.2.1 Combine and . Step 5.2.2 Move the negative in front of the fraction....
a-z Shows the alphabet. trig Shows the trigonometry functions. ◀ Move the cursor left. ▶ Move the cursor right. ▲ Move the cursor up. ▼ Move the cursor down. □□ Exponent. □2 Squared. □□ Fraction. □ Square Root. □□ Nth Root. (□) Parenthesis. log Log base 10. ln ...
Apply basic rules ofexponents. Tap for more steps... Rewrite1x2as(x2)-1. 9ddx[(x2)-1] thein(x2)-1. Apply theand,(am)n=amn. 9ddx[x2⋅-1] 2by-1. 9ddx[x-2] 9ddx[x-2] 9ddx[x−2]9ddx[x-2] Differentiate using thePower Rulewhich states thatddx[xn]ddx[xn]isnxn...
Step 5 Simplify. Tap for more steps... Step 5.1 Rewrite the expression using the negative exponent rule . Step 5.2 Combine terms. Tap for more steps... Step 5.2.1 Combine and . Step 5.2.2 Move the negative in front of the fraction....