( e^td/(dt)[e^(2t)-e^(-2t)]+(e^(2t)-e^(-2t))d/(dt)[e^t]) By the Sum Rule, the derivative of ( e^(2t)-e^(-2t)) with respect to ( t) is ( d/(dt)[e^(2t)]+d/(dt)[-e^(-2t)]). ( e^t(d/(dt)[e^(2t)]+d/(dt)[-e^(-2t)])+(e
Find the Derivative Using Product Rule - d/du h(u)=(u- square root of u)(u+ square root of u) ( h(u)=(u-√u)(u+√u)) 相关知识点: 试题来源: 解析 Differentiate using the Product Rule which states that ( d/(du)[f(u)g(u)]) is ( f(u)d/(du)[g(u)]+g(u)d/(du...
Find the derivative of F(z)=(16z4+4z2+1)(4z3−z) using the product rule. Integration:In the product rule, differentiate a separate function each time and after that add both the terms. Thereafter, the concluding result is given in an uncomplicated form. ...
Step 1 Differentiate using the Product Rule which states that is where and .Step 2 By the Sum Rule, the derivative of with respect to is .Step 3 Evaluate . Tap for more steps... Step 3.1 Use to rewrite as . Step 3.2 Differentiate using the Power Rule which states that is where . ...
Find the derivative using the derivative rules A. {eq}y ( x ) = 2 x ^ { 3 } \operatorname { cos } ( x ) {/eq} B. {eq}y ( x ) = ( 2 x ^ { 4 } + 6 ) e ^ { x } {/eq} Product Rule: If we have two differentiable fu...
Find the Derivative Using Product Rule - d/dr (d^2)/(dr^2)(pir^2)( (d^2)/(dr^2)(π r^2
Differentiate using the Product Rule which states that ( d/(dt)[f(t)g(t)]) is ( f(t)d/(dt)[g(t)]+g(t)d/(dt)[f(t)]) where ( f(t)=t^(20)) and ( g(t)=(ln)(|t|)).( t^(20)d/(dt)[(ln)(|t|)]+(ln)(|t|)d/(dt)[t^(20)])Differentiate using the chain...
Answer to: Find the derivative of a function using the product rule, quotient rule, or chain rule with basic derivative rules. Find D_z (3 z^2 - 17...
1. Identify the Functions: Let u(x)=ex and v(x)=cosx. 2. Differentiate u(x): The derivative of u(x)=ex is: u′(x)=ex 3. Differentiate v(x): The derivative of v(x)=cosx is: v′(x)=−sinx 4. Apply the Product Rule: Now, using the product rule: f′(x)=u′(x)v...
The product rule of derivative is a method to find the derivative of two functions when they are given in product form. Suppose we have y=uv then from the product rule dydx=udvdx+vdudx. Answer and Explanation: Given: The function is y=(x+5)(x+5). Note t...